This class describes the displacement operator defined on the points of the mesh. More...

#include <EMM_DisplacementFEMOperator.h>

Inheritance diagram for EMM_DisplacementFEMOperator:

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Collaboration diagram for EMM_DisplacementFEMOperator:

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Public Member Functions
virtual tBoolean	discretize (const EMM_LandauLifschitzSystem &system)
	discretize the operator More...

virtual tBoolean	resetToInitialState (const EMM_LandauLifschitzSystem &system)
	reset the operator to initial state the operator More...

void	setMassMatrixType (const tFlag &t)
	set the mass matrix type More...

const tFlag &	getMassMatrixType () const
	get the mass matrix type More...

virtual SP::EMM_MassMatrix	NewMassMatrix () const
	create the accelerator matrix More...

const tUIndex *	getPointsNumber () const
	get the points number in each direction More...

const tCellFlag &	getPeriodicIndicator () const
	get the periodicity indication More...

const EMM_CellFlagArray &	getNeighborsIndicator () const
	return the neighbors indicator in bits $\displaystyle \sum_{f=0}^{f=F-1} v_f 2^f$ where F is the number of faces per element and is 1 if there is a neighbor cell with the face f More...

virtual tULLInt	getMemorySize () const
	return the memory size in byte More...

virtual tBoolean	getDataFieldSpace (const tUSInt &index, tString &dataName, tFlag &supportType, tString &dFieldType, tUIndex &n, tDimension &dim) const
	get the data field at index for saving data in vtk,txt,... files. More...

virtual void	computeEquilibriumMatrixDiagonalConditioner (MATH_Vector &D) const
	compute the diagonal conditioner More...

virtual tReal	computeCineticEnergy (const EMM_RealField &V) const
	compute the energy of the magnetostriction operator at current displacement and velocity More...

virtual tReal	computePotentialEnergy (const EMM_RealField &U) const
	compute the potential energy to the space variation of the displacement More...

tReal	computeStressConstraintEnergy (const EMM_RealField &Uf) const
	compute the stress constraint energy on boundary More...

virtual tString	toString () const
	turn the martix into string More...

virtual void	adimensionize (const tReal &Le, const tReal &Ms, const tReal &T, const tReal &L)
	adimensionize the operator More...

const tReal *	getAdimensionizedSegmentsSize () const
	get the segments size in all directions More...

const EMM_RealArray &	getAdimensionizedVolumicMass () const
	get the adimensionized volumic mass per cell More...

const EMM_4SymmetricTensors &	getLambdaE () const
	return the adimensionized elastic tensor distribution $\lambda^e$ More...

const EMM_4Tensors &	getLambdaEDoubleDotLambdaM () const
	return the adimensionized magnetic tensor distribution $\lambda^e:\lambda^m$ More...

const EMM_4Tensors &	getLambdaMDoubleDotLambdaE () const
	return the adimensionized magnetic tensor distribution $\lambda^m:\lambda^e$ More...

const EMM_4SymmetricTensors &	getLambdaMDoubleDotLambdaEDoubleDotLambdaM () const
	return the adimensionized magnetic tensor distribution $\lambda^m:\lambda^e:\lambda^m$ More...

void	setInitialDisplacement (const tReal &scale, const tString &dataFile)
	set initial displacement field. More...

void	setInitialDisplacement (const tReal data[3])
	set initial displacement field More...

void	setInitialDisplacement (const tReal U0, const tReal &U1, const tReal &U2)
	set initial displacement field More...

void	setInitialDisplacement (const EMM_RealField &data)
	set initial displacement field More...

void	setInitialVelocity (const tReal &scale, const tString &dataFile)
	set initial velocity field More...

void	setInitialVelocity (const EMM_RealField &data)
	set initial velocity field More...

void	setInitialVelocity (const tReal data[3])
	set initial velocity field More...

void	setInitialVelocity (const tReal &V0, const tReal &V1, const tReal &V2)
	set initial velocity field More...

void	setLimitConditionOnPoints (const EMM_IntArray &lc)
	set the limit condition each point is set to More...

void	setLimitConditionOnPoints (const tLimitCondition &lc)
	set the limit condition to all points More...

void	setConstraints (const tFlag &C, const tString &dataFile)
	set constraints from file defined on points More...

void	setConstraints (const tFlag &C, const tReal data[3])
	set constraints field More...

void	setConstraints (const tFlag &C, const tReal &C0, const tReal &C1, const tReal &C2)
	set initial constriants field More...

void	setConstraints (const tFlag &C, const EMM_RealField &data)
	set constraints More...

const tFlag &	getConstraintFaces () const
	get the constraint faces $C=\sum_{f=0}^{f=5} C_f 2^f$ if face f is constrainted More...

const EMM_RealField &	getConstraints () const
	get the constraints field for reading More...

EMM_RealField &	getConstraints ()
	get the constraints field for writing More...

const EMM_LimitConditionArray &	getLimitConditionOnPoints () const

SPC::EMM_LimitConditionArray	getLimitConditionOnPointsByReference () const

void	nullProjectionOnDirichletBoundary (EMM_RealField &V) const
	project the velocity to 0 on dirichlet boundary points More...

void	nullProjectionOnDirichletBoundary (const tUIndex &nPoints, const tDimension &dim, tReal *V) const
	project the velocity to 0 on dirichlet boundary points More...

void	projectionOnDirichletBoundary (const EMM_RealField &V0, EMM_RealField &V) const
	project the velocity to 0 on dirichlet boundary points More...

void	projectionOnDirichletBoundary (const tUIndex &nPoints, const tDimension &dim, const tBoolean &incV0, const tReal V0, tReal V) const
	project the velocity to 0 on dirichlet boundary points More...

void	periodicProjection (const tCellFlag &periodicity, const tUInteger nPoints[3], EMM_RealField &V) const
	make the periodic projection of the field V More...

virtual tBoolean	backup (const tString &prefix, const tString &suffix, const tString &ext) const
	backup of the operator data into file(s) used for restoring More...

virtual tBoolean	restore (const EMM_LandauLifschitzSystem &system, const tString &prefix, const tString &suffix, const tString &ext)
	restore the operator data from file(s) More...

const EMM_2PackedSymmetricTensors &	getElasticTensor () const
	return the elastic tensor $\varepsilon(u)=\displaystyle \frac{1}{2} \left ( \frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i} \right )$ More...

virtual tUSInt	getDataFieldsNumber () const
	get the number of field used in the operator More...

virtual tBoolean	getDataField (const tUSInt &index, tString &dataName, tUIndex &n, tDimension &dim, const float *&values) const
	get the data field at index for saving data in vtk,txt,... files. More...

virtual tBoolean	getDataField (const tUSInt &index, tString &dataName, tUIndex &n, tDimension &dim, const double *&values) const
	get the data field at index for saving data in vtk,txt,... files. More...

virtual tBoolean	getDataField (const tUSInt &index, tString &dataName, tUIndex &n, tDimension &dim, const long double *&values) const
	get the data field at index for saving data in vtk,txt,... files. More...

virtual tBoolean	isAffine () const
	return true if the operator is either constant or linear More...

virtual tBoolean	isGradientComputationable () const
	return true if the gradient of the magnetic excitation is computationable More...

void	setDisplacement (const EMM_RealField &u)
	set the displacement field More...

void	setDisplacement (const tReal &Ux, const tReal &Uy, const tReal &Uz)
	set the displacement field to an uniform vector defied on points More...

EMM_RealField &	getDisplacement ()
	get the displacement for writing More...

const EMM_RealField &	getDisplacement () const
	get the displacement for reading More...

const EMM_RealField &	getDisplacement (const tReal &t) const
	get the veolicty at time More...

void	setVelocity (const EMM_RealField &v)
	set the velocity of dicplacement defined on points More...

void	setVelocity (const tReal &Vx, const tReal &Vy, const tReal &Vz)
	set the displacement velocity field to an uniform vector defined on points More...

EMM_RealField &	getVelocity ()
	get the velocity for writing More...

const EMM_RealField &	getVelocity (const tReal &t) const
	get the velocity at time More...

const EMM_RealField &	getVelocity () const
	get the velocity at t for reading More...

EMM_RealField &	getAccelerator ()
	get the accelerator for writing More...

const EMM_RealField &	getAccelerator () const
	get the accelerator for reading More...

virtual void	setSolver (const tString &solverName)
	set the solver More...

void	setSolver (SP::MATH_Solver solver)
	set the solver More...

MATH_Solver *	getSolver ()
	get the solver of the system More...

void	setElasticityState (const tFlag &v)
	set the elasticity state More...

tBoolean	isSteadyState () const

tBoolean	isEquilibriumState () const

tBoolean	isFrozenState () const

void	setTimeIntegrationMethod (const tFlag &m)
	set the time integration method for new field More...

const tFlag &	getTimeIntegrationMethod () const
	get the time integration method for next time step More...

void	setTimeIntegrationOrder (const tInt &o)
	set the time integration order for new field More...

const tUCInt &	getTimeIntegrationOrder () const
	get the time integration order for new field More...

const tReal &	getTimeStep () const
	get the time step for elasticty More...

void	setCFL (const tReal &cfl)
	set the cfl for computing the initial time step More...

virtual tBoolean	computeFieldsAtTime (const tReal &t, const tFlag &order, const EMM_RealArray &sigma, const EMM_RealField &dM_dt0, const EMM_RealField &M0)
	compute the fields of operator at time More...

virtual tBoolean	updateAtNextTimeStep (const tReal &dt, const EMM_RealArray &sigma, const EMM_RealField &Mt)
	update the data of operator at next time step More...

virtual SP::EMM_BlockEquilibriumMatrix	NewEquilibriumMatrix () const
	create the equilibrium matrix More...

void	setIsEquilibriumMatrixReconditioned (const tBoolean &c)
	set to true if the equilibrium matrix is conditioned More...

const tBoolean &	isEquilibriumMatrixReconditioned () const
	get if the equilibrium matrix is conditioned More...

tBoolean	computeEquilibriumState (const EMM_RealArray &sigma, const EMM_RealField &M, const EMM_RealField &U0, EMM_RealField &U)
	compute the equilibirum state $div(\lambda^e:epsilon(U))=div(\lambda^e:\lambda^m:M \otimes M)$ More...

virtual void	computeElasticStressMatrixProduct (const tUIndex &nData, const tDimension &dim, const tReal U, tReal D) const
	compute the elastic stress Matrix product $A.U = - div \left (\tilde \lambda^e : \varepsilon(u) \right )$ More...

virtual void	computeElasticTensor (const EMM_RealField &U, EMM_2PackedSymmetricTensors &eTensor)
	compute the elastic tensor for all cells $\epsilon(U)=\frac{1}{2} \left (\nabla U + \nabla^t U \right )$ More...

void	computeStress (const EMM_RealArray &sigma, const EMM_RealField &U, const EMM_RealField &M, EMM_RealField &stress) const
	compute the stress $div(sigma(U,M))=div(\lambda^e:\epsilon(U))-div(\lambda^2:\lambda^m:M\otimes M)$ More...

virtual void	computeElasticStress (const EMM_RealField &U, EMM_RealField &S) const
	compute the elastic stress for all cells $div(\lambda^e:\epsilon(U))$ More...

void	computeElasticStress (const tUIndex &nData, const tDimension &dim, const tReal U, tReal D) const
	compute the elastic stress $S_e(u) =div \left (\tilde \lambda^e : \varepsilon(u) \right )$ More...

void	computeMagneticStress (const EMM_RealArray &sigma, const EMM_RealField &M, EMM_RealField &S) const
	compute the magnetic stress for all cells $S=div(\lambda^e:\lambda^m:M\otimes M)$ More...

virtual void	computeMagneticStress (const tReal &alpha, const tReal &beta, const EMM_RealArray &sigma, const EMM_RealField &M, EMM_RealField &S) const =0
	compute the magnetic stress for all cells from the stress $S=alphaS+betadiv(\lambda^e:\lambda^m:M\otimes M)$ More...

tReal	computeEnergy (const tReal &t, const tUIndex &nCells, const tDimension &dim, const EMM_RealArray &sigma, const tReal *M) const
	compute the energy of the magnetostriction operator at current displacement and velocity More...

tReal	computeCineticEnergyAtTime (const tReal &t) const
	compute the energy due to velocity More...

tReal	computePotentialEnergyAtTime (const tReal &t) const
	compute the potential energy to the space variation of the displacement More...

tReal	computeStressConstraintEnergy (const tReal &t) const
	compute the energy of the boundary stress constraint More...

virtual tString	getName () const
	return an human reading name of the operator More...

const tBoolean &	isCubicVolume () const
	return the true if the element is cubic More...

const tReal &	getElementVolume () const
	return the adimensionized volume of the element More...

void	getSharedPointer (SP::CORE_Object &p)
	get the shared pointer of this class into p More...

void	getSharedPointer (SPC::CORE_Object &p) const
	get the shared pointer of this class into p More...

tString	getClassName () const
	return the class name of the object More...

tString	getIdentityString () const
	return the identity string of the object of the form className_at_address More...

tString	getPointerAddress () const
	return the identity string of the object More...

template<class T >
tBoolean	isInstanceOf () const
	test if the clas T is an instance of this class More...

tBoolean	isInstanceOf (const tString &name) const
	test if the object is an instance of className More...

Static Public Member Functions
static void	setIsMemoryChecked (const tBoolean &v)
	set if the memory checking is used More...

static void	setOut (SP::CORE_Out out)
	set the output stream More...

static void	resetOut ()
	reset the output stream More...

static void	setThread (SP::CORE_Thread thread)
	set the thread More...

static void	resetThread ()
	reset the output stream More...

static CORE_Out &	out ()
	get the output More...

static SP::CORE_Out	getOut ()
	get the output More...

static CORE_Thread &	getThread ()
	get the profilier More...

static const tBoolean &	isMemoryChecked ()
	get if the memory checking is used More...

static tString	getClassName (const tString &identityString)
	return the class name of the object More...

template<class T >
static tString	getTypeName ()
	get type name More...

static tBoolean	is64Architecture ()
	return true if the machine is a 64 bits machine More...

static tBoolean	is32Architecture ()
	return true if the machine is a 32 bits machine More...

static tString	pointer2String (const void *obj)
	return the string representation of a pointer More...

static void	printObjectsInMemory (ostream &f)
	print object in memory More...

static void	printObjectsInMemory ()
	print object in memory in the standart output More...

static tChar	getMaxChar ()
	get the max value for tChar type More...

static tChar	getMinChar ()
	get the min value for tChar type More...

static tUChar	getMaxUChar ()
	get the max value for tUChar type More...

static tUChar	getMinUChar ()
	get the min value for tUChar type More...

static tSInt	getMaxSInt ()
	get the max value for tSInt type More...

static tSInt	getMinSInt ()
	get the min value for tSInt type More...

static tUSInt	getMaxUSInt ()
	get the max value for tUSInt type More...

static tUSInt	getMinUSInt ()
	get the min value for tUSInt type More...

static tInt	getMaxInt ()
	get the max value for tInt type More...

static tInt	getMinInt ()
	get the min value for tInt type More...

static tUInt	getMaxUInt ()
	get the max value for tUInt type More...

static tUInt	getMinUInt ()
	get the min value for tUInt type More...

static tLInt	getMaxLInt ()
	get the max value for tLInt type More...

static tLInt	getMinLInt ()
	get the min value for tLInt type More...

static tULInt	getMaxULInt ()
	get the max value for tULInt type More...

static tULInt	getMinULInt ()
	get the min value for tULInt type More...

static tLLInt	getMaxLLInt ()
	get the max value for tULInt type More...

static tLLInt	getMinLLInt ()
	get the min value for tLLInt type More...

static tULLInt	getMaxULLInt ()
	get the max value for tULLInt type More...

static tULLInt	getMinULLInt ()
	get the min value for tULLInt type More...

static tFloat	getMaxFloat ()
	get the max value for tFloat type More...

static tFloat	getMinFloat ()
	get the min value for tFloat type More...

template<class T >
static T	getEpsilon ()
	get the epsilon value for T type More...

template<class T >
static T	getInfinity ()
	get the infinity for T type More...

static tFloat	getFloatEpsilon ()
	get the epsilon value for tFloat type More...

static tFloat	getFloatInfinity ()
	get the infinity value for tFloat type More...

static tDouble	getMaxDouble ()
	get the max value for tDouble type More...

static tDouble	getMinDouble ()
	get the min value for tDouble type More...

static tDouble	getDoubleInfinity ()
	get the infinity value for tFloat type More...

static tDouble	getDoubleEpsilon ()
	get the epsilon value for tDouble type More...

static tLDouble	getMinLDouble ()
	get the min value for tLDouble type More...

static tLDouble	getMaxLDouble ()
	get the max value for tLDouble type More...

static tLDouble	getLDoubleEpsilon ()
	get the epsilon value for tLDouble type More...

static tDouble	getLDoubleInfinity ()
	get the infinity value for tDouble type More...

static tIndex	getMaxIndex ()
	get the max value for the array/vector indexing type More...

static tIndex	getMinIndex ()
	get the min value for the array/vector indexing type More...

static tUIndex	getMaxUIndex ()
	get the max value for difference the array/vector indexing type More...

static tUIndex	getMinUIndex ()
	get the min value for difference the array/vector indexing type More...

static tFlag	getMaxFlag ()
	get the max value for the tFlag type More...

static tFlag	getMinFlag ()
	get the min value for the tFlag type More...

static tUInteger	getMaxUInteger ()
	get the max value for the unsigned integer type More...

static tUInteger	getMinUInteger ()
	get the min value for the unsigned integer type More...

static tInteger	getMaxInteger ()
	get the max value for the integer type More...

static tInteger	getMinInteger ()
	get the min value for the integer type More...

static tReal	getMaxReal ()
	get the max value for the real type More...

static tReal	getMinReal ()
	get the min value for the real type More...

static tReal	getRealEpsilon ()
	get the eps which is the difference between 1 and the least value greater than 1 that is representable. More...

static tReal	getRealInfinity ()
	get the infinity value More...

template<class T >
static T	computeEpsilon ()
	compute epsilon More...

Static Public Attributes
static const tFlag	CANONICAL_MASS_MATRIX =0
	mass matrix whose each element is real More...

static const tFlag	BLOCK_MASS_MATRIX =1
	mass matrix whose each element is a digonal matrixof size 3 More...

static const tFlag	CONDENSED_MASS_MATRIX =2
	mass matrix is diagonal More...

static const tFlag	P1 =1

static const tFlag	TE =0

static const tFlag	FROZEN_STATE =1

static const tFlag	EQUILIBRIUM_STATE =3

static const tFlag	UNSTEADY_STATE =0

static const tReal	Mu0 =4M_PI1e-07

static const tReal	Gamma =-1.7e11

static const tDimension	X =0

static const tDimension	Y =1

static const tDimension	Z =2

static const tReal	NULL_VALUE [] ={0,0,0}

Protected Member Functions
	EMM_DisplacementFEMOperator (void)
	create More...

virtual	~EMM_DisplacementFEMOperator (void)
	destroy More...

virtual void	buildDataOnBoundaryFaces (const EMM_Grid3D &mesh, const EMM_LimitConditionArray &limitConditionOnPoints, const EMM_RealField &U0, EMM_RealField &DnU0)
	build the data on boundary faces More...

virtual tBoolean	solveAcceleratorSystem (EMM_RealField &V)
	solve the velocity form the accelerator matrix : M.X=V V:=X More...

virtual void	spaceProjection (EMM_RealField &V) const
	make the projection of the vector B into the solving linear space More...

virtual void	spaceProjection (const EMM_RealField &V0, EMM_RealField &V) const
	make the projection of the vector B into the solving linear space More...

virtual void	spaceRelevant (EMM_RealField &V) const
	make the rebuild of the vector V from the solving space. More...

virtual void	computeElasticTensor (const tUIndex &nData, const tDimension &dim, const tReal *U, EMM_2PackedSymmetricTensors &eTensor) const
	compute the elastic tensor for all cells More...

virtual void	computeElasticStress (const tBoolean &withConstraints, const tReal &beta, const tUIndex &nData, const tDimension &dim, const tReal U, tReal D) const
	compute the elastic stress $S_e(u) = \beta * div \left (\tilde \lambda^e : \varepsilon(u) \right )$ More...

virtual void	computeMagneticStress (const tReal &alpha, const tReal &beta, const tUIndex &nCells, const tDimension &dim, const EMM_RealArray &sigma, const tReal M, const tUIndex &nData, tReal D) const
	compute the magnetic stress $S=\alpha S + \beta * div \left (\sigma^2 . \tilde \lambda^2 : ( \lambda^m : m \otimes m ) \right )$ to elastic stress S More...

virtual void	toDoAfterThisSetting ()
	method called after the setting of the shared pointer this method can only be called once. More...

virtual void	initializeEquilibriumSolver (const EMM_RealField &U0)
	initialize the equilibrium solver More...

void	setThis (SP::CORE_Object p)
	set this weak shared pointer called toDoAfterThis setting method More...

Private Member Functions
	SP_OBJECT (EMM_DisplacementFEMOperator)

tBoolean	buildDataOnNeumannBoundaryFaces (const EMM_Grid3D &mesh, const EMM_LimitConditionArray &limitConditionOnPoints, const EMM_RealField &DnU0, EMM_RealField &C) const
	build the data on boundary faces More...

void	addBoundaryElasticStress (const tReal &beta, const tUIndex &nPoints, const tDimension &dim, tReal *D) const
	add the elastic stress from boundary More...

Private Attributes
tFlag	mMassMatrixType

SP::EMM_MassMatrix	mMassMatrix

Static Private Attributes
static const tCInt	INT_GRAD_PHI []

static const tUCInt	INT_GRAD_PHI_FACTOR =4

Detailed Description

This class describes the displacement operator defined on the points of the mesh.

It solves the adimensionzed equations by finite element method:

$\displaystyle \kappa \frac{\partial^2 u}{\partial t^2} = div( \tilde \lambda^e:\epsilon(u)) - div( \sigma^2(x) \tilde \lambda^e:\tilde \lambda^m : m \otimes m )$

with

on dirichlet points and
$(\tilde \lambda^e : \varepsilon(u) ) .N = C$ on Neuman points

To compute the normalized displacement $ u $ , we multiply by an arbitrary function $ v $ the conservation of momentum normalized equation and by integrating in the whole normalized domain and after using the green formula, for dirichlet problem v $\in R^3$ where v=0 on $\partial \omega_0$ , we obtain by taking into account the Neumann condition on $\partial \omega_1$ , $\left ( \lambda^e:\epsilon(U) - \lambda^e:\lambda^m : M \otimes M \right ) \cdot n = C$

$\displaystyle \int_\omega \frac{\partial^2 u}{\partial t^2} v d\omega = - \int_\omega \left ( \tilde \lambda^e:\epsilon(u) \right): \nabla v d\omega + \int_{\partial \omega_1} v. \left ( \tilde \lambda^e : \varepsilon(u) \right ). N d\sigma +$

$\int_\omega \left (\tilde \lambda^e:\tilde \lambda^m:m \otimes m \sigma^2(x) \right ) : \nabla v d\omega$

With the applied forces, it becomes:

$\displaystyle \int_\omega \frac{\partial^2 u}{\partial t^2} v d\omega = - \int_\omega \left ( \tilde \lambda^e:\epsilon(u) \right): \nabla v d\omega + \int_{\partial \omega_1} v. C d\sigma +$

$\int_\omega \left (\tilde \lambda^e:\tilde \lambda^m:m \otimes m \sigma^2(x) \right ) : \nabla v d\omega$

The 3d-variable $ u(t,x)=[u_0(t,x),u_1(t,x),u_2(t,x)] $ is decomposed in $ R^3 $ with $\displaystyle u_k(t,x)=\sum_{p=0}^{p=N-1} u_p^k(t) \Phi_p(x)$ where N is the number of points of the mesh of the magnetized domain, $\Phi_p$ is the Q1 base element : $\Phi_p(x,y,z)=c_7.xyz+c_6.xy+c_5.yz+c_4.xz+c_3.x+c_2.y+c_1.z+c_0$ which is null in all the mesh points except at the point p where its value is 1.

The points of the mesh is composed by

a set of interior points denoted by I
a set of Neumann points denoted by $\Gamma_n$
a set of Dirichlet points denoted by $\Gamma_d$
a set of periodical points where
- $\Gamma_s$ is the set of slave periodical points
- $\Gamma_m$ is the set of master periodical points : $\forall p \in \Gamma_s, \exists q \in \Gamma_m , q-p=t$ where t is the periodicity
the set of all points $P=I \cup \Gamma_n \cup \Gamma_d \cup \Gamma_p$

We can have a Dirichlet condition on periodical faces : $\Gamma_p \cap \Gamma_d \neq \emptyset$ .

$\forall q \in J=I \cup \Gamma_n \cup \Gamma_m$ , on all free points, we take $v=\Phi_q$ , the k-coordinate projection, we have (as $\tilde \lambda^e_{ijkl}=\tilde \lambda^e_{ijlk}$ ):

$\displaystyle \frac{d^2}{dt^2}\int_\omega u_k(t,x) \Phi_q(x) d\omega = - \int_\omega \sum_{jst} \left ( \tilde \lambda^e_{kjst} \frac{\partial u_s }{\partial x_t } \frac{\partial \Phi_q }{\partial x_j } \right ) d\omega + \int_{\Gamma_n} C_k (x) \cdot \Phi_q d\sigma + \displaystyle \int_\omega \left ( \sum_{jstli} \tilde \lambda^e_{kjst} \tilde \lambda^m_{stli} \sigma^2(x) m_l m_i \frac{\partial \Phi_q }{\partial x_j }\right ) d\omega$

The magnetized domain is discretized with M parallelepiped cells, $\omega = \displaystyle \bigcup_{c=0}^{c=M-1} \omega_c$ , $\Gamma_n = \displaystyle \bigcup_{f=0}^{f=F-1} \gamma_f$ .

$\displaystyle \frac{d^2}{dt^2} \left ( \sum_{p \in N } u_p^k(t) \sum_{c=0}^{M-1} \int_{\omega_c} \Phi_p(x) \Phi_q(x) d\omega \right ) = - \sum_{p \in N} \sum_{c=0}^{M-1} \int_{\omega_c} \sum_{jst} \left ( \tilde \lambda^e_{kjst} u_p^s(t)\frac{\partial \Phi_p }{\partial x_t } \frac{\partial \Phi_q }{\partial x_j } \right ) d\omega + \sum_{f=0}^{F-1} \int_{\gamma_f} C^k_p \Phi_p \cdot \Phi_q d\sigma + \displaystyle \sum_{c=0}^{M-1} \int_{\omega_c} \left ( \sum_{jstli} \tilde \lambda^e_{kjst} \tilde \lambda^m_{stli} \sigma_i^2 m_l m_i \frac{\partial \Phi_q }{\partial x_j }\right ) d\omega$

On the discretized domain, we obtain the system , $\forall k \in \{0,1,2\}, \forall q \in J$ :

$\displaystyle \frac{d^2}{dt^2} \sum_{p \in N } M_{pq} U_{3p+k}(t) = \sum_{p \in N } \sum_{s \in \{0,1,2\}} A_{3q+k,3p+s}.U_{3p+s}(t) =B_{3q+k}(M) + C_{3q+k}$ where

$\displaystyle M_{q,p}=\sum_{c=0}^{M-1} \int_{\omega_c} \Phi_p(x) \Phi_q(x) d\omega_c$ see EMM_MassMatrix::product()
$\displaystyle A_{3q+k,3p+s}= - \sum_{c \in [0,M[} \sum_{jt\in \{0,1,2\}^2} \tilde \lambda^e_{kjst} \int_{\omega_c} \frac{\partial \Phi_p }{\partial x_t } \frac{\partial \Phi_q }{\partial x_j } d\omega_c$ see EMM_DisplacementFEMOperator::computeElasticStress()
$\displaystyle B_{3q+k}(M) =\sum_{c \in [0,M[} \sum_{j,s,t,l,i \in \{0,1,2\}^5} \tilde \lambda^e_{kjst} \tilde \lambda^m_{stli} \sigma_i^2 m_l m_i \int_{\omega_c} \frac{\partial \Phi_q }{\partial x_j }d\omega_c$ see EMM_DisplacementFEMOperator::computeMagneticStress()
$\displaystyle C_{3q+k}=\sum_{f=0}^{F-1} \int_{\gamma_f} C^k_p (x) \Phi_p \cdot \Phi_q d\sigma$ see EMM_DisplacementFEMOperator::addBoundaryElasticStress() called in EMM_DisplacementFEMOperator::computeMagneticStress()
is the mean value of the magnetism at cell $\omega_c$
$\tilde \lambda^m$ is the value of the variable taken at the cells $\omega_c$ which contains point p and/or q
$\tilde \lambda^e$ is the value of the variable taken at the cells $\omega_c$ which contains point p and/or q
$M_{q,p}$ is a matrix of size |J| x |N|
$U_{3p+k}(t)=u^k_p, \forall k \in \{0,1,2\}, \forall p \in N$ of size 3.|N|
$A_{3q+k,3p+s}$ is a matrix of size 3|J| x 3|N|, s in [0,3[
$B_{3q+k}$ is a vector of size 3.|J| , $\forall q \in [0,N[, \forall k \in [0,3[$
$C_{3q+k}$ is a vector of size 3.|J| , $\forall q \in [0,N[, \forall k \in [0,3[$

So we have:

$\displaystyle \forall q \in J, \frac{d^2}{dt^2} \sum_{p \in N } \sum_{s \in \{0,1,2\}} M_{3q+k,3p+s} U_{3p+s}(t) = \sum_{p \in N } \sum_{s \in \{0,1,2\}} A_{3q+k,3p+s}.U_{3p+s}(t)+B_{3q+k}(M)+C_{3q+k}$

where M_{p,q} is defined by a mass block matrix whose block is $I_3 $ :

$M_{3q+k,3p+s}=C_{q,p} \delta_{ks}$ with $\delta_{ks}=1$ if and only if $ k=s $ .

The linear equation to solve is :

$\displaystyle \frac{d^2}{dt^2} M.U(t) = A.U(t)+B(M(t)) +C$

The time step scheme is given by a taylor expansion of order 2 with time step $dt_n=t^{n+1}-t^n$ and with $\eta=\frac{dt_n}{dt_{n-1}}$

$\frac{\partial^2 U}{\partial t^2}= \displaystyle \frac{2. \eta}{(\eta+1) \cdot dt_{n}^2} \left ( U^{n+1}+\eta. U^{n-1}-(1+\eta).U^n \right )$

we solve the linear system : $ M . W = S $ where $S= \left ( B- A \cdot U^n \right)$

and we deduce the new value of the displacment field thanks to W :

$U^{n+1} = \frac{(\eta+1)\cdot.dt_{n}^2}{2\eta} W +(1+\eta) U^n - \eta U^{n-1}$ .

This formulation leads to a non squared matrix. In order to inverse rapidly the matrix M , the matrix is turned into a symmetric definite positive squared matrix by adding diagonal rows on linked points in $\Gamma_f \cup \Gamma_s$ :

$\forall q \in N \setminus J , M_{3q+k,3p+s}= \delta_{pq}.\delta{ks}$ and

$\forall q \in N \setminus J , S_{3q+k}= 0$

to ensure that $W_{3q+k}=0$ after resolving the linear system.

Then U is rebuild by the formulas :

$U^{n+1}_{3.q+k} = \frac{(\eta+1)\cdot.dt_{n}^2}{2\eta} W_{3.q+k} +(1+\eta) U^n_{3q+k} - \eta U^{n-1}_{3q+k} = U^0_{3q+k}$ , for Dirichlet points q
$U^{n+1}_{3.s+k} = U^{n+1}_{3.m+k} \forall s \in \Gamma_s$ and m is the associated periodical point in $\Gamma_m$ .

So to solve the U we use the following algorithm:

compute the S vector of size 3.|N|
make a projection of S on the solving space $\forall q \in \Gamma_d \cup \Gamma_s, \forall k \in \{0,1,2\}, S_{3q+k}=0$
solve the system of size |N|^2, by the gradient conjugate method. Note that only the Matrix Vector product needs to be implemented.
rebuild the vector W from the solving space $\forall s \in \Gamma_s, \exists m \in \Gamma_m , \forall k \in \{0,1,2\}, W_{3s+k}=W_{3m+k}$ .
compute U from W by the formula $\forall q \in N, \forall k \in \{0,1,2\}, U^{n+1}_{3.q+k} = \frac{(\eta+1)\cdot.dt_{n}^2}{2\eta} W_{3.q+k} +(1+\eta) U^n_{3q+k} - \eta U^{n-1}_{3q+k}$ .

Note that if we have a Dirichlet condition depending on time (not implemented yet), the projection of S of the solving space will impose to set :

$\forall q \in \Gamma_d, \forall k \in \{0,1,2\}, S_{3q+k}=\frac{2\eta}{(\eta+1) \cdot dt_{n}^2} \left ( U^0(t_{n+1},3q+k)+\eta. U_{3q+k}^{n-1}-(1+\eta).U^n_{3q+k} \right ) \neq 0$

To reduce the size of the system, a map from N into J may be built but it will need more memory size to store the map and it is not sure that a lot of CPU time may be saved (not implemented).

To compute the equilibrium state we have to solve the equations : $\displaystyle div( \tilde \lambda^e:\epsilon(u)) - div( \sigma^2(x) \tilde \lambda^e:\tilde \lambda^m : m \otimes m ) = 0$

with

on dirichlet points and
$(\tilde \lambda^e : \varepsilon(u) ) .N = C$ on Neuman points

The weak formulation gives :

$\displaystyle - \int_\omega \left ( \tilde \lambda^e:\epsilon(u) \right): \nabla v d\omega + \int_{\partial \omega_1} v. \left ( \tilde \lambda^2 : \varepsilon(u) \right ). N d\sigma +$

$\int_\omega \left (\tilde \lambda^e:\tilde \lambda^m:m \otimes m \sigma^2(x) \right ) : \nabla v d\omega = 0$

In order to ensure the definite positive of the operator, we put it in the form : $\displaystyle \int_\omega \left ( \tilde \lambda^e:\epsilon(u) \right): \nabla v d\omega = \int_{\partial \omega_1} v. C d\sigma +$

$\int_\omega \left (\tilde \lambda^e:\tilde \lambda^m:m \otimes m \sigma^2(x) \right ) : \nabla v d\omega$

The discrete formulation is

$\sum_{p \in N } \sum_{s \in \{0,1,2\}} A_{3q+k,3p+s}.U_{3p+s}(t) = B_{3q+k}(M) + C_{3q+k}$ where

$\displaystyle A_{3q+k,3p+s}= \sum_{c \in [0,M[} \sum_{jt\in \{0,1,2\}^2} \tilde \lambda^e_{kjst} \int_{\omega_c} \frac{\partial \Phi_p }{\partial x_t } \frac{\partial \Phi_q }{\partial x_j } d\omega_c$ see EMM_DisplacementFEMOperator::computeElasticStress()
$\displaystyle B_{3q+k}(M) =\sum_{c \in [0,M[} \sum_{j,s,t,l,i \in \{0,1,2\}^5} \tilde \lambda^e_{kjst} \tilde \lambda^m_{stli} \sigma_i^2 m_l m_i \int_{\omega_c} \frac{\partial \Phi_q }{\partial x_j }d\omega_c$ see EMM_DisplacementFEMOperator::computeMagneticStress()
$\displaystyle C_{3q+k}=\sum_{f=0}^{F-1} \int_{\gamma_f} C^k_p (x) \Phi_p \cdot \Phi_q d\sigma$ see EMM_DisplacementFEMOperator::addBoundaryElasticStress() called in EMM_DisplacementFEMOperator::computeMagneticStress()

To compute $\displaystyle \int_{\omega_c} \Phi_p \Phi_q d\omega$ , $\displaystyle \int_{\omega_c} \frac{\partial \Phi_p }{\partial x_l } \frac{\partial \Phi_q }{\partial x_j } d\omega$ or $\displaystyle \int_{\omega_c} \frac{\partial \Phi_q }{\partial x_j }d\omega$ , $\displaystyle \int_{\gamma_f} \Phi_p \Phi_q d\gamma$ , each cell $\omega_c \subset \omega$ and each $\gamma_f \subset \Gamma_n$ of the mesh is transformed into the referenced cell in $[0,1]\times[0,1]\times[0,1]$ with reference nodes $P_0=(0,0,0)$ , $P_1=(1,0,0)$ , $P_2=(0,1,0)$ , $P_3=(1,1,0)$ , $P_4=(0,0,1)$ , $P_5=(1,0,1)$ , $P_6=(0,1,1)$ , $P_7=(1,1,1)$ by the transform function $ T(r,s,t)=(N^0_0+h_0.r,N^1_0+h_1.s,N_0^2+h_2.t) $ where $r,s,t \in [0,1]^3=\hat{\omega}$ , $ N_0 $ if the base corner (min point) of the mesh cell $\omega_c$ , and $ h_0,h_1,h_2 $ , the size of the cell mesh $ w_c $ .

The corresponding reference base function $\displaystyle \hat{\Phi_i}$ on the cell 's point $ P_i $ is given by $\displaystyle \Phi_i(P_j)=\delta_{ij}$ .

The integral is transformed into a referenced cell: $\displaystyle \int_{{\omega_c}} \frac{\partial \Phi_q }{\partial x_j }d{\omega_c} = |\omega_c| \int_{\hat{\omega}} \frac{\partial \hat{\Phi_q} }{\partial r_j }\frac{1}{h_j} d{\hat{\omega}}$ where $|\omega_c| = h_0.h_1.h_2$ by normalization.

The computation $\int_{\hat{\omega}} \frac{\partial \hat{\Phi_q} }{\partial r_j }d\hat{\omega}$ is done as follow:

$\begin{tabular}{llllllll} $ i $ & $ \displaystyle \hat{\Phi_i}$ & $ \displaystyle \frac{\partial \hat{\Phi_i}}{\partial r} $ & $ \displaystyle \frac{\partial \hat{\Phi_i}}{\partial s} $ & $ \displaystyle \frac{\partial \hat{\Phi_i}}{\partial t} $ & $ \displaystyle \int_{\hat{\omega}} \frac{\partial \hat {\Phi_i}}{\partial r }d\hat{\omega}$ & $ \displaystyle \int_{\hat{\omega}} \frac{\partial \hat {\Phi_i}}{\partial s }d\hat{\omega}$ & $ \displaystyle \int_{\hat{\omega}} \frac{\partial \hat {\Phi_i}}{\partial t }d\hat{\omega}$ \\ $0$ & $ \displaystyle (1-r)(1-s)(1-t)$ & $ \displaystyle (1-s)(t-1)$ & $ \displaystyle (1-r)(t-1)$ & $ \displaystyle (1-r)(s-1)$ & $ \displaystyle -\frac{1}{4}$ & $ \displaystyle -\frac{1}{4}$ & $ \displaystyle -\frac{1}{4}$ \\ $1$ & $ \displaystyle r(1-s)(1-t)$ & $ \displaystyle (1-s)(1-t)$ & $ \displaystyle r(t-1)$ & $ \displaystyle r(s-1)$ & $ \displaystyle \frac{1}{4}$ & $ \displaystyle -\frac{1}{4}$ & $ \displaystyle -\frac{1}{4}$ \\ $2$ & $ \displaystyle (1-r)s(1-t)$ & $ \displaystyle s(t-1)$ & $ \displaystyle (1-r)(1-t)$ & $ \displaystyle (r-1)s$ & $ \displaystyle -\frac{1}{4}$ & $ \displaystyle \frac{1}{4}$ & $ \displaystyle -\frac{1}{4}$ \\ $3$ & $ \displaystyle rs(1-t)$ & $ \displaystyle s(1-t)$ & $ \displaystyle r(1-t)$ & $ \displaystyle -rs$ & $ \displaystyle \frac{1}{4}$ & $ \displaystyle \frac{1}{4}$ & $ \displaystyle -\frac{1}{4}$ \\ $4$ & $ \displaystyle (1-r)(1-s)t$ & $ \displaystyle (s-1)t$ & $ \displaystyle (r-1)t$ & $ \displaystyle (1-r)(1-s)$ & $ \displaystyle -\frac{1}{4}$ & $ \displaystyle -\frac{1}{4}$ & $ \displaystyle \frac{1}{4}$ \\ $5$ & $ \displaystyle r(1-s)t$ & $ \displaystyle (1-s)t$ & $ \displaystyle -rt$ & $ \displaystyle r(1-s)$ & $ \displaystyle \frac{1}{4}$ & $ \displaystyle -\frac{1}{4}$ & $ \displaystyle \frac{1}{4}$ \\ $6$ & $ \displaystyle (1-r)st$ & $ \displaystyle -st$ & $ \displaystyle (1-r)t$ & $ \displaystyle (1-r)s$ & $ \displaystyle -\frac{1}{4}$ & $ \displaystyle \frac{1}{4}$ & $ \displaystyle \frac{1}{4}$ \\ $7$ & $ \displaystyle rst$ & $ \displaystyle st$ & $ \displaystyle rt$ & $ \displaystyle rs$ & $ \displaystyle \frac{1}{4}$ & $ \displaystyle \frac{1}{4}$ & $ \displaystyle \frac{1}{4}$ \end{tabular}$

We can compress formula by $\hat \Phi_p(x_0,x_1,x_2)=\displaystyle \prod_{k=0}^{k=2} (1-x_k)^{1-p_k}\cdot x_k^{p_k}$ where $\displaystyle p=\sum_{k=0}^{k=2} p_k.2^k=(p_0,p_1,p_2)$ , base point of the reference element.

Then we have $\displaystyle \frac{\partial \hat \Phi_p}{\partial x_i }=(-1)^{1-p_i} \prod_{k=0,k\neq i}^{k=2} (1-x_k)^{1-p_k} \cdot x_k^{p_k}$ .

So we have $\displaystyle \int_{\hat \omega} \frac{\partial \hat \Phi_q }{\partial x_j }d{\hat \omega} = \displaystyle (-1)^{1-q_j} \frac{1}{4}$ with $ q=(q_0,q_1,q_2)$

It can be rewritten as $\displaystyle \int_{\omega_c} \frac{\partial \Phi_q }{\partial x_j }d{\omega_c} = \frac{h_0.h_1.h_2}{4.h_j} . D_ {qj}$ where D is the matrix 8x3:

$\begin{tabular}{lll} -1 & -1 & -1 \\ 1 & -1 & -1 \\ -1 & 1 & -1 \\ 1 & 1 & -1 \\ -1 & -1 & 1 \\ 1 & -1 & 1 \\ -1 & 1 & 1 \\ 1 & 1 & 1 \\ \end{tabular}$

To compute the following integrals, we note that :

$\int_0^1 (1-x)^2dx=\frac{1}{3}$
$\int_0^1 x^2dx=\frac{1}{3}$
$\int_0^1 x.(1-x)dx=\frac{1}{6}$
$\forall p \in\{0,1\}, \int_0^1 (1-x)^{1-p}.x^pdx=\frac{1}{2}$

So, $\int_0^1 (1-x)^{2-p} \cdot x^p dx=I(p)$ where

$I(0)=\frac{1}{3}$
$I(1)=\frac{1}{6}$
$I(2)=\frac{1}{3}$

So $I(p)=\frac{1}{6}\cdot (|p-1|+1)$

So to compute $\displaystyle \int_{\omega_c} \frac{\partial \Phi_p}{\partial x_i}\frac{\partial \Phi_q}{\partial x_j} d\omega_c=\displaystyle \frac{h_0.h_1.h_2}{h_i.h_j} \int_{\hat \omega } \frac{\partial \hat \Phi_p}{\partial x_i}\frac{\partial \hat \Phi_q}{\partial x_j} d{hat \omega}$ .

$\forall p,q \in [0,7]^2, \forall i \neq j , \int_{\hat \omega } \frac{\partial \hat \Phi_p}{\partial x_i}\frac{\partial \hat \Phi_q}{\partial x_j} d{\hat \omega} = \displaystyle \frac{1}{6.2.2} \cdot (-1)^{p_i+q_j} \cdot (|p_k+q_k-1|+1)$ , k is the only value in {0,1,2} different from i and j.

$\forall p,q \in [0,7]^2, \forall i \int_{\hat \omega } \frac{\partial \hat \Phi_p}{\partial x_i}\frac{\partial \hat \Phi_q}{\partial x_i} d{\hat \omega} = \displaystyle \frac{1}{6.6} \cdot (-1)^{p_i+q_i} \cdot \prod_{k=0,k\neq i}^{k=2} (|p_k+q_k-1|+1)$ .

To compute the constraint matrix, $\displaystyle C_{p,q} = \displaystyle \int_{\Gamma_n} \Phi_p(x) \Phi_q(x) d{\gamma} = \sum_{\gamma_f | P_p,P_q \in \gamma_f^2} \displaystyle \int_{\gamma_f} \Phi_p(x) \Phi_q(x) d{\gamma}$

$\displaystyle \int_{\gamma_f} \Phi_p(x) \Phi_q(x) d{\gamma} = \prod_{k=0,k \neq l}^{k=2} h_k. \int_0^1 \hat \Phi_p(x_0,x_1,x_2) \cdot \hat \Phi_q(x_0,x_1,x_2) dx_k$ where the normal of the face f is on the l-direction. But,

$\displaystyle \prod_{k=0,k \neq l}^{k=2} h_k. \int_0^1 \hat \Phi_p(x_0,x_1,x_2) \cdot \hat \Phi_q(x_0,x_1,x_2) dx_k =$

$(1-x_l)^{2-(p_l+q_l)}\cdot x_l^{p_l+q_l} \prod_{k=0,k \neq l}^{k=2} h_k \cdot \int_0^1 (1-x_k)^{2-(p_k+q_k)}\cdot x_k^{p_k+q_k} dx_k$ .

As we have:

$\displaystyle \int_0^1 (1-x_k)^{2-(p_k+q_k)}\cdot x_k^{p_k+q_k} dx_k = I(p_k+q_k)=\frac{1}{6}\cdot ( |pk+qk-1|+1)$

we conclude

$\displaystyle \int_{\gamma_f} \Phi_p(x) \Phi_q(x) d{\gamma} = \frac{1}{36} \cdot \prod_{k=0,k\neq l}^{k=2} h_k. (|p_k+q_k-1|+1)$

To compute the mass matrix, $\displaystyle M_{p,q}=\displaystyle \int_{\omega} \Phi_p(x) \Phi_q(x) d{\omega} = \sum_{\omega_c | P_p,P_q \in \omega_c^2} \displaystyle h_0.h_1.h_2. \int_0^1 \int_0^1 \int_0^1 \hat \Phi_p(x_0,x_1,x_2) \hat \Phi_q(x_0,x_1,x_2) dx_0.dx_1.dx_2$

$\displaystyle \int_0^1 \int_0^1 \int_0^1 \hat \Phi_p(x_0,x_1,x_2) \hat \Phi_q(x_0,x_1,x_2) dx_0.dx_1.dx_2 = \displaystyle \int_0^1 \int_0^1 \int_0^1 \prod_{k=0}^{k=2} (1-x_k)^{1-p_k-q_k}\cdot x_k^{p_k+q_k} dx_0.dx_1.dx_2$

$\displaystyle \int_0^1 \int_0^1 \int_0^1 \hat \Phi_p(x_0,x_1,x_2) \hat \Phi_q(x_0,x_1,x_2) dx_0.dx_1.dx_2 = \displaystyle \prod_{k=0}^{k=2} I(p_k+q_k)$

$\displaystyle \int_0^1 \int_0^1 \int_0^1 \hat \Phi_p(x_0,x_1,x_2) \hat \Phi_q(x_0,x_1,x_2) dx_0.dx_1.dx_2 = \displaystyle \frac{1}{6^3} \prod_{k=0}^{k=2} \left (|p_k+q_k-1|+1\right )$

$\displaystyle \int_0^1 \int_0^1 \int_0^1 \hat \Phi_p(r,s,t) \hat \Phi_q(r,s,t) dr.ds.dt = \displaystyle \frac{1}{6^3} \Delta_{p,q}$

where $\Delta$ is a column packed symmetric matrix matrix 8x8:

$\begin{tabular}{lllllllll} p,q & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ 0 & 8 & 4 & 4 & 2 & 4 & 2 & 2 & 1 \\ 1 & 4 & 8 & 2 & 4 & 2 & 4 & 1 & 2 \\ 2 & 4 & 2 & 8 & 4 & 2 & 1 & 4 & 2 \\ 3 & 2 & 4 & 4 & 8 & 1 & 2 & 2 & 4 \\ 4 & 4 & 2 & 2 & 1 & 8 & 4 & 4 & 2 \\ 5 & 2 & 4 & 1 & 2 & 4 & 8 & 2 & 4 \\ 6 & 2 & 1 & 4 & 2 & 4 & 2 & 8 & 4 \\ 7 & 1 & 2 & 2 & 4 & 2 & 4 & 4 & 8 \\ \end{tabular}$

If we use the mean formula of integration $\displaystyle \int_0^1 (1-x)^{2-(p_k+q_k)}.x^{p_k+q_k} dx = \frac{1}{2}.\left( (1-1)^{2-(p_k+q_k)}.1^{p_k+q_k} + (1-0)^{2-(p_k+q_k)}.0^{p_k+q_k} \right )$ ,

we have $\displaystyle \int_0^1 (1-x)^{2-(p_k+q_k)}.x^{p_k+q_k} dx = \delta_{p_k,q_k} . \frac{1}{2}$ .

So $\displaystyle M_{p,q}=\displaystyle \sum_{\omega_c | P_p,P_q \in \omega_c^2} \int_{\omega_c} \Phi_p(x) \Phi_q(x) d{\omega_c} = \displaystyle \sum_{ \omega_c | P_p,P_q \in \omega_c^2} | \cdot h_0.h_1.h_2.\frac{1}{8} \delta_{p,q}$ with is a diagonal matrix called Condensed Mass matrix.

The K & M matrix are computing during the discretization step because they do not evolutate during the relaxation process.

The normalized energy of this implemented displacement class is reduced to its cinetic energy:

$e_m(m)=\displaystyle +\frac{1}{4} \int_\omega |\frac{\partial u}{\partial t}|^2d\omega$

The velocity verifies by using a Taylor expansion of order 2 in time with $\eta=\displaystyle \frac{t_{n+1}-t_n}{t_n-t_{n-1}}=\frac{dt_n}{dt_{n-1}}$

$\frac{\partial u}{\partial t} = \displaystyle \frac{1}{dt \cdot (\eta+1)} \cdot \left ( u(t_{n+1})-\eta^2 u(t_{n-1}) -(1-\eta^2) u(t_n) \right )$

@author Stephane Despreaux
@version 1.0

Constructor & Destructor Documentation

◆ EMM_DisplacementFEMOperator()

EMM_DisplacementFEMOperator::EMM_DisplacementFEMOperator ( void )

protected

create

References BLOCK_MASS_MATRIX, and mMassMatrixType.

◆ ~EMM_DisplacementFEMOperator()

EMM_DisplacementFEMOperator::~EMM_DisplacementFEMOperator ( void )

protectedvirtual

destroy

Member Function Documentation

◆ addBoundaryElasticStress()

void EMM_DisplacementFEMOperator::addBoundaryElasticStress	(	const tReal &	beta,
		const tUIndex &	nPoints,
		const tDimension &	dim,
		tReal *	D
	)		const

private

add the elastic stress from boundary

Parameters

[in]	beta	: multiplicator of Boundary Stress B
[in]	nPoints	number of points
[in]	dim	dimension of the problem in [1,3]
[in,out]	D	the elastic stress of size nPoints*dim

D+=beta.B with $B=\int_{partial omega} C.\phi d\sigma$

References EMM_DisplacementOperator::getConstraints(), CORE_Object::getThread(), CORE_Thread::getThreadsNumber(), null, OMP_GET_THREAD_ID, OMP_PARALLEL_PRIVATE_SHARED_DEFAULT, tDimension, tReal, tUIndex, and tUInteger.

Referenced by computeElasticStress(), and getDataFieldSpace().

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◆ adimensionize()

virtual void EMM_DisplacementOperator::adimensionize	(	const tReal &	Le,
		const tReal &	Ms,
		const tReal &	T,
		const tReal &	L
	)

inlinevirtualinherited

adimensionize the operator

Parameters

[in]	Le	common elasticity adimensionized parameter
[in]	Ms	common magnetization at saturation
[in]	T	caracterictic time
[in]	L	caracteristic length

adimensionize the associated displacement operator

Reimplemented from EMM_Operator.

◆ backup()

tBoolean EMM_DisplacementOperator::backup	(	const tString &	prefix,
		const tString &	suffix,
		const tString &	ext
	)		const

virtualinherited

backup of the operator data into file(s) used for restoring

Parameters

prefix	: common prefix of the saving files
suffix	: common suffix of the saving files
ext	: common extension of the saving files

Returns: true if the saving of the U & V file have succeeded

It saves

the current time step in {prefix}_dt_{suffix}.{ext}
U at previous time step in {prefix}_Unm1_{suffix}.{ext}
U at current time step in {prefix}_Un_{suffix}.{ext}
V at current time step in {prefix}_Vn_{suffix}.{ext}
dV/dt at current time step in {prefix}_Acc_{suffx}.{ext}

Reimplemented from EMM_Operator.

Reimplemented in EMM_DisplacementFVMOperator.

References EMM_DisplacementOperator::isEquilibriumState(), EMM_DisplacementOperator::isFrozenState(), EMM_DisplacementOperator::mAccelerator, EMM_DisplacementOperator::mDt, EMM_DisplacementOperator::mEpsilonUt, EMM_DisplacementOperator::mTimeIntegrationMethod, EMM_DisplacementOperator::mUn, EMM_DisplacementOperator::mUnm1, EMM_DisplacementOperator::mVn, CORE_Object::out(), CORE_Out::println(), EMM_Tensors::saveToFile(), tBoolean, EMM_DisplacementOperator::TE, and tString.

Referenced by EMM_DisplacementFVMOperator::backup(), and EMM_DisplacementOperator::getLimitConditionOnPointsByReference().

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◆ buildDataOnBoundaryFaces()

virtual void EMM_DisplacementFEMOperator::buildDataOnBoundaryFaces	(	const EMM_Grid3D &	mesh,
		const EMM_LimitConditionArray &	limitConditionOnPoints,
		const EMM_RealField &	U0,
		EMM_RealField &	DnU0
	)

inlineprotectedvirtual

build the data on boundary faces

Parameters

mesh	the mesh of the domain
limitConditionOnPoints	: limit condition on points
U0	: U at all points at t=0
DnU0	: grad UO . N at each point slave Naumann points and Neumann points

recompute the DnUO with the formula :

if q is not a Neumann points
$C^d_q= \sum_{f | q \in \gamma_f } \sum_{p | p \in \gamma_f} (D_nU^0)^d_p \frac{1}{36} \cdot \prod_{k=0,k\neq l}^{k=2} h_k. (|p_k+q_k-1|+1)$ where the l is the direction of the normal to $\gamma_f$

Implements EMM_DisplacementOperator.

References buildDataOnNeumannBoundaryFaces(), EMM_RealField::copy(), discretize(), EMM_RealField::NewInstance(), resetToInitialState(), EMM_RealField::setSize(), and tBoolean.

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◆ buildDataOnNeumannBoundaryFaces()

tBoolean EMM_DisplacementFEMOperator::buildDataOnNeumannBoundaryFaces	(	const EMM_Grid3D &	mesh,
		const EMM_LimitConditionArray &	limitConditionOnPoints,
		const EMM_RealField &	DnU0,
		EMM_RealField &	C
	)		const

private

build the data on boundary faces

Parameters

mesh	the mesh of the domain
limitConditionOnPoints	: limit condition on points
DnU0	: grad UO . N at each point
C	: the constraint of ach point of the mesh

compute the constraint on each point of the mesh with the formula :

if q is not a Neumann points
$C^d_q= \sum_{f | q \in \gamma_f } \sum_{p | p \in \gamma_f} (D_nU^0)^d_p \frac{1}{36} \cdot \prod_{k=0,k\neq l}^{k=2} h_k. (|p_k+q_k-1|+1)$ where the l is the dierction of the normal to $\gamma_f$
Returns
false if U is null

periodicity of the domain

start=iq+Px.(jq+Py.kq)

References EMM_Grid3D::ELEMENT_POINTS, EMM_Grid3D::FACE_POINTS, EMM_Grid3D::GET_MASTER_PERIODIC_POINT(), EMM_DisplacementOperator::getAdimensionizedSegmentsSize(), EMM_DisplacementOperator::getConstraintFaces(), EMM_RealField::getDimension(), EMM_Grid3D::getNeighborsIndicators(), EMM_Grid3D::getPeriodicIndicator(), EMM_Grid3D::getSegmentsNumber(), EMM_RealField::getSize(), CORE_Object::getThread(), CORE_Thread::getThreadsNumber(), EMM_RealField::getValues(), EMM_Grid3D::getVerticesNumber(), iand, EMM_RealField::initField(), EMM_Grid3D::IS_ELEMENT_MAGNETIZED(), EMM_Grid3D::NEUMANN_LIMIT_CONDITION, null, OMP_GET_THREAD_ID, OMP_PARALLEL_PRIVATE_SHARED_DEFAULT_REDUCTION, EMM_Grid3D::POINTS_NUMBER_PER_ELEMENT, EMM_Grid3D::POINTS_NUMBER_PER_FACE, EMM_RealField::setDimension(), EMM_RealField::setSize(), EMM_Grid3D::SLAVE_LIMIT_CONDITION, tBoolean, tCellFlag, tDimension, tFlag, tInteger, tLimitCondition, tReal, tUCInt, tUIndex, tUInteger, and tUSInt.

Referenced by buildDataOnBoundaryFaces().

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◆ computeCineticEnergy()

tReal EMM_DisplacementFEMOperator::computeCineticEnergy ( const EMM_RealField & V ) const

virtual

compute the energy of the magnetostriction operator at current displacement and velocity

Parameters

V velocity

Returns: cinetic energy value $\int_\omega |\frac{\partial u}{\partial t}|(t) ^2 d\omega$

Implements EMM_DisplacementOperator.

References EMM_DisplacementOperator::getAdimensionizedVolumicMass(), EMM_RealField::getSize(), and mMassMatrix.

Referenced by getDataFieldSpace().

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◆ computeCineticEnergyAtTime()

tReal EMM_DisplacementOperator::computeCineticEnergyAtTime ( const tReal & t ) const

inlineinherited

compute the energy due to velocity

Parameters

t	time in [0,dt[ where dt is the time step

Returns: cinetic energy value $\int_\omega |\frac{\partial u}{\partial t}|(t) ^2 d\omega$

References EMM_DisplacementOperator::computeCineticEnergy(), EMM_DisplacementOperator::getVelocity(), and tReal.

Referenced by EMM_DisplacementOperator::computeEnergy().

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◆ computeElasticStress() [1/3]

void EMM_DisplacementFEMOperator::computeElasticStress	(	const tBoolean &	withConstraints,
		const tReal &	beta,
		const tUIndex &	nData,
		const tDimension &	dim,
		const tReal *	U,
		tReal *	D
	)		const

protectedvirtual

compute the elastic stress $S_e(u) = \beta * div \left (\tilde \lambda^e : \varepsilon(u) \right )$

Parameters

withConstraints	: if true compute the whore opertaor if false, compute only the linear part of operator
beta	factor of the strees to turn intto definite positive/negative matrix
nData	number of data for U (nCells or nVertices depending on the method)
dim	dimension of the problem in [1,3]
U	the displacement field values
D	the elastic stress of size nData*dim

$S_e(u) = - \beta \sum_{c \in [0,M[} \sum_{jt\in \{0,1,2\}^2} \tilde \lambda^e_{kjst} \int_{\omega_c} \frac{\partial \Phi_p }{\partial x_t } \frac{\partial \Phi_q }{\partial x_j } d\omega_c$

It is an affine operator $ S_e(U)= A. U + B.U_0 + C.F $ where

A is symmetric definite positive which is the linear part of the affine operator
is the constant part of the affine operator
- is the Dirichlet values of the field
- is the applied forces

start=iq+Px.(jq+Py.kq)

Implements EMM_DisplacementOperator.

References addBoundaryElasticStress(), EMM_Grid3D::DIRICHLET_LIMIT_CONDITION, EMM_Grid3D::ELEMENT_POINTS, EMM_Grid3D::GET_MASTER_PERIODIC_POINT(), EMM_DisplacementOperator::getAdimensionizedSegmentsSize(), EMM_Operator::getElementVolume(), EMM_DisplacementOperator::getLambdaE(), EMM_DisplacementOperator::getLimitConditionOnPoints(), getNeighborsIndicator(), getPeriodicIndicator(), getPointsNumber(), EMM_4Tensors::getTensorSize(), CORE_Object::getThread(), CORE_Thread::getThreadsNumber(), EMM_Grid3D::IS_ELEMENT_MAGNETIZED(), EMM_Tensors::isNotNull(), null, OMP_GET_THREAD_ID, OMP_PARALLEL_PRIVATE_SHARED_DEFAULT, EMM_Grid3D::POINTS_NUMBER_PER_ELEMENT, EMM_Grid3D::SLAVE_LIMIT_CONDITION, tBoolean, tCellFlag, tDimension, tFlag, tInteger, tLimitCondition, tReal, tUCInt, tUIndex, and tUInteger.

Referenced by EMMG_DisplacementFEMOperator::computeElasticStress(), and getDataFieldSpace().

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◆ computeElasticStress() [2/3]

virtual void EMM_DisplacementOperator::computeElasticStress	(	const EMM_RealField &	U,
		EMM_RealField &	S
	)		const

inlinevirtualinherited

compute the elastic stress for all cells $div(\lambda^e:\epsilon(U))$

Parameters

U	the displacement field
S	the elastic stress field

It computes:

$\forall (i,k) \in [0,N[\times[0,d[, S^i_k= \displaystyle div(\lambda^e:\varepsilon(u^i))_k = \displaystyle \sum_{l=0}^{d-1} \frac{\partial \left( \displaystyle \sum_{r,s=0}^{r,s=d-1} \lambda^e_{klrs} \frac{\partial u^i_s}{\partial x_r} \right )}{\partial x_l}$ where

is the s-coordinate of the displacement u at cell i when s is in [0,d[ and d is the dimension of the space (i.e. 3).
is the r-coordinate of points in cell

Reimplemented in EMMG_DisplacementFVM_VOGGROperator, EMMG_DisplacementFVM_SSGROperator, EMMG_DisplacementFVM_STEGROperator, EMMG_DisplacementFVM_VTEGROperator, and EMMG_DisplacementFEMOperator.

References EMM_RealField::getDimension(), EMM_RealField::getValues(), tDimension, tReal, and tUIndex.

Referenced by EMM_DisplacementOperator::computeElasticStress(), EMM_DisplacementOperator::computeElasticStressMatrixProduct(), EMM_DisplacementOperator::computeStress(), and EMM_DisplacementOperator::initializeEquilibriumSolver().

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◆ computeElasticStress() [3/3]

void EMM_DisplacementOperator::computeElasticStress	(	const tUIndex &	nData,
		const tDimension &	dim,
		const tReal *	U,
		tReal *	D
	)		const

inlineinherited

compute the elastic stress $S_e(u) =div \left (\tilde \lambda^e : \varepsilon(u) \right )$

Parameters

nData	number of data for U (nCells or nVertices depending on the method)
dim	dimension of the problem in [1,3]
U	the displacement field values
D	the elastic stress of size nData*dim

It computes $S^i_e(u) = - \displaystyle \int_\Omega \left (\tilde \lambda^e : \varepsilon(u) \right ) : \nabla \phi^i d\Omega$

$\forall d \in [0,3[, \forall q \in [0,P[, B[3q+d]= \displaystyle - \sum_{c \in V(P_q)} \int_{\omega_c} \sum_{p=0}^{p=8} \sum_{lrs} \left ( \lambda^c_{dlrs} u_{i_P}^s(t)\frac{\partial \Phi_p }{\partial x_r } \frac{\partial \Phi_q }{\partial x_l} \right ) d\omega$

where $i_P $ is the index of the p-th point into cell $\omega_c$ , P is the number of interior magnetized points and $ V(P_q) $ is the set of cells connected to point q.

Algorithm:

D=0, initialize to 0
pts={[0,0,0],[1,0,0],[0,1,0],[1,1,0],[0,0,1],[1,0,1],[0,1,1],[1,1,1]} local coordinates of cell points.
- - index of the cell c
  - if iCell is in magnetized domain
    - $\lambda^e=getLambda^e(iCell)$ of size 3x3x3x3
    - loop on nodes of cell iCell of local coordinate .
      - iP is the global index of local point p
      - iP=(i+Px)+Nx*(j+Py)+Nx.Ny.(k+Pz)
      - $\forall (d,l,r,s)\in R^4, D_{i_Q,d}-=\lambda^e_{klrs}.D_{pqrl}.U^{i_P}_s$ with
        
        $D_{pqrr}=\frac{h_0.h_1.h_2}{h^2_r} . \frac{1}{36}. (-1)^{p_r+q_r} . \prod_{k=0}^{k=2} (|p_k+q_k-1|+1)$
        
        $D_{pqrl}=\frac{h_0.h_1.h_2}{h_r.h_l}.\frac{1}{24}. (-1)^{p_r+q_l} . (|p_k+q_k-1|+1) k \neq l, k \neq r$

References EMM_DisplacementOperator::computeElasticStress(), tBoolean, tDimension, tReal, and tUIndex.

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◆ computeElasticStressMatrixProduct()

virtual void EMM_DisplacementOperator::computeElasticStressMatrixProduct	(	const tUIndex &	nData,
		const tDimension &	dim,
		const tReal *	U,
		tReal *	D
	)		const

inlinevirtualinherited

compute the elastic stress Matrix product $A.U = - div \left (\tilde \lambda^e : \varepsilon(u) \right )$

Parameters

nData	number of data for U (nCells or nVertices depending on the method)
dim	dimension of the problem in [1,3]
U	the displacement field values
D	the elastic stress of size nData*dim

make the computation of A.U=-S_e.U for the elastic equilibrium matrix product with null constraints

Reimplemented in EMM_DisplacementFVM_VIGROperator.

References EMM_DisplacementOperator::computeElasticStress(), EMM_DisplacementOperator::computeElasticTensor(), tDimension, tReal, and tUIndex.

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◆ computeElasticTensor() [1/2]

void EMM_DisplacementFEMOperator::computeElasticTensor	(	const tUIndex &	nData,
		const tDimension &	dim,
		const tReal *	U,
		EMM_2PackedSymmetricTensors &	eTensor
	)		const

protectedvirtual

compute the elastic tensor for all cells

Parameters

nData	size of the displacement field
dim	dimension of the displacement field
U	values of the displacement field
eTensor	the elastic tensor of size 3x3 stored in column-packed symmetric upper matrix array of size 6

$\forall (r,s) \in [0,3[^2, \varepsilon_{rs}= \displaystyle \frac{1}{2}\left ( \frac{\partial u_r}{\partial x_s} + \frac{\partial u_s}{\partial x_r} \right )=eTensor[r+(s*(s+1)/2)]$ where

is the r-coordinate of the displacement u
is the s-coordinate of point in cell

The finite element approximation of $\frac{\partial u_r}{\partial x_s}$ at cell i , is given by

$\displaystyle \frac{\partial u_r}{\partial x_s} = \displaystyle \frac{1}{|\omega|} \int_\omega \frac{\partial u_r}{\partial x_s} d\omega = \displaystyle \sum_{q=0}^{q=7} u_q^r \frac{D_{qs}}{4.h_s}$ where $\displaystyle \frac{D_{qs}}{4}=\int_{\hat \omega} \frac{\partial \hat \Phi_q }{\partial r_s }d{\hat \omega}$

$\varepsilon_{ks}$ is computed as follow in a packed symmetric column storage at cell i :

for all k in [0,3 [
- $\displaystyle \frac{dU^i_s}{dx_k}= \sum_{q=0}^{q=7} u_q^k \frac{D_{qs}}{4.h_s}$
- for all s in [0,k[, $\varepsilon_{ks} += \frac{1}{2}.\frac{dU^i_s}{dx_k}$
- $\varepsilon_{kk} = \frac{dU^i_k}{dx_k}$
- for all s in ]k,3[, $\varepsilon_{sk} += \frac{1}{2}. \frac{dU^i_s}{dx_k}$

Implements EMM_DisplacementOperator.

References CORE_MorseArray< T >::begin(), EMM_Grid3D::ELEMENT_POINTS, CORE_MorseArray< T >::fitToSize(), EMM_DisplacementOperator::getAdimensionizedSegmentsSize(), CORE_MorseArray< T >::getIndices(), getNeighborsIndicator(), getPointsNumber(), CORE_Array< T >::getSize(), EMM_2PackedSymmetricTensors::getTensorSize(), EMM_Tensors::getTensorsNumber(), CORE_Object::getThread(), CORE_Thread::getThreadsNumber(), EMM_Tensors::getValues(), INT_GRAD_PHI, INT_GRAD_PHI_FACTOR, EMM_Grid3D::IS_ELEMENT_MAGNETIZED(), OMP_GET_THREAD_ID, OMP_PARALLEL_PRIVATE_SHARED_DEFAULT, EMM_Grid3D::POINTS_NUMBER_PER_ELEMENT, EMM_Tensors::setTensorsNumber(), tBoolean, tCellFlag, tCInt, tDimension, tReal, tUCInt, tUIndex, tUInteger, and CORE_MorseArrayIterator< T >::values().

Referenced by getDataFieldSpace().

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◆ computeElasticTensor() [2/2]

void EMM_DisplacementOperator::computeElasticTensor	(	const EMM_RealField &	U,
		EMM_2PackedSymmetricTensors &	eTensor
	)

virtualinherited

compute the elastic tensor for all cells $\epsilon(U)=\frac{1}{2} \left (\nabla U + \nabla^t U \right )$

Parameters

U	the displacement field
eTensor	the elastic tensor of size 3x3 stored in row-packed symmetric upper matrix array of size 6

$\forall (r,s) \in [0,3[^2, \varepsilon_{rs}= \displaystyle \frac{1}{2}\left ( \frac{\partial u_r}{\partial x_s} + \frac{\partial u_s}{\partial x_r} \right )=eTensor[r+(s*(s+1)/2)]$ where

is the r-coordinate of the displacement u
is the s-coordinate of point in cell

Reimplemented in EMM_DisplacementFVMOperator, and EMM_DisplacementFVM_VIGROperator.

References EMM_RealField::getDimension(), EMM_RealField::getValues(), tDimension, tReal, and tUIndex.

Referenced by EMM_DisplacementOperator::computeElasticStressMatrixProduct(), EMM_DisplacementFVMOperator::computeElasticTensor(), EMM_DisplacementOperator::computeFieldsAtTime(), EMM_DisplacementOperator::restore(), and EMM_DisplacementOperator::updateAtNextTimeStep().

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◆ computeEnergy()

tReal EMM_DisplacementOperator::computeEnergy	(	const tReal &	t,
		const tUIndex &	nCells,
		const tDimension &	dim,
		const EMM_RealArray &	sigma,
		const tReal *	M
	)		const

inherited

compute the energy of the magnetostriction operator at current displacement and velocity

Parameters

t	the time in [0,dt[ where dt is the time step
nCells	: number of cells
dim	dimension of each point of mesh
sigma	the weight of each cell
M	the magnetization field values

Returns: energy value : $E(m,u)=\displaystyle \frac{1}{2} \int_\omega \sigma^4(x)[\tilde \lambda^e:(\tilde \lambda^m:m \otimes m)]:(\tilde \lambda^m:m \otimes m) d\omega$ $\displaystyle -\int_\omega \sigma^2(x) \epsilon(u):(\tilde \lambda^e:(\tilde \lambda^m:m \otimes m)) d\omega$ $\displaystyle +\frac{1}{2} \int_\omega (\tilde \lambda^e:\epsilon(u)):\epsilon(u) d\omega$ $\displaystyle +\frac{1}{2} \int_\omega |\frac{\partial u}{\partial t}|^2d\omega$

References EMM_DisplacementOperator::computeCineticEnergyAtTime(), EMM_DisplacementOperator::computePotentialEnergyAtTime(), EMM_DisplacementOperator::computeStressConstraintEnergy(), EMM_DisplacementOperator::getConstraints(), EMM_DisplacementOperator::getElasticTensor(), EMM_Operator::getElementVolume(), CORE_Array< T >::getSize(), CORE_Object::getThread(), EMM_DisplacementOperator::isEquilibriumState(), EMM_DisplacementOperator::mLme, CORE_Thread::startChrono(), tBoolean, tReal, and tString.

Referenced by EMM_MagnetostrictionOperator::computeEnergy(), and EMM_DisplacementOperator::computeMagneticStress().

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◆ computeEpsilon()

template<class T >

static T CORE_Object::computeEpsilon ( )

inlinestaticinherited

compute epsilon

Returns: the epsilon value eps=10^{-p/3} where p is defined by getEpsilon()=10^{-p}

◆ computeEquilibriumMatrixDiagonalConditioner()

void EMM_DisplacementFEMOperator::computeEquilibriumMatrixDiagonalConditioner ( MATH_Vector & D ) const

virtual

compute the diagonal conditioner

Parameters

[out] D is the diagonal conditioner of the equilibrium matrix by defualt the diagonal matrix is the identity (its size if set to 0);

start=iq+Px.(jq+Py.kq)

Reimplemented from EMM_DisplacementOperator.

References EMM_Grid3D::DIRICHLET_LIMIT_CONDITION, EMM_Grid3D::ELEMENT_POINTS, EMM_DisplacementOperator::getAdimensionizedSegmentsSize(), EMM_RealField::getDimension(), EMM_DisplacementOperator::getDisplacement(), EMM_Operator::getElementVolume(), EMM_DisplacementOperator::getLambdaE(), EMM_DisplacementOperator::getLimitConditionOnPoints(), getNeighborsIndicator(), getPeriodicIndicator(), getPointsNumber(), EMM_4Tensors::getTensorSize(), CORE_Object::getThread(), CORE_Thread::getThreadsNumber(), MATH_Vector::getValues(), EMM_Grid3D::IS_ELEMENT_MAGNETIZED(), EMM_DisplacementOperator::isEquilibriumMatrixReconditioned(), EMM_Tensors::isNotNull(), OMP_GET_THREAD_ID, OMP_PARALLEL_PRIVATE_SHARED_DEFAULT, EMM_Grid3D::POINTS_NUMBER_PER_ELEMENT, MATH_Vector::setSize(), EMM_Grid3D::SLAVE_LIMIT_CONDITION, tBoolean, tCellFlag, tDimension, tFlag, tInteger, tLimitCondition, tReal, tUCInt, tUIndex, and tUInteger.

Referenced by getDataFieldSpace().

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◆ computeEquilibriumState()

tBoolean EMM_DisplacementOperator::computeEquilibriumState	(	const EMM_RealArray &	sigma,
		const EMM_RealField &	M,
		const EMM_RealField &	U0,
		EMM_RealField &	U
	)

inherited

compute the equilibirum state $div(\lambda^e:epsilon(U))=div(\lambda^e:\lambda^m:M \otimes M)$

Parameters

[in]	sigma	: the weight array due to unhomegeneous magnetization at saturation
[in]	M	: the magnetization field
[in]	U0	: the displacement field at dirichlet point
[out]	U	the dispacement field at equilibrium

Returns

true if the solving succeeds

compute the right hand side of the equation
make a projection of W into f the solving space (W=U0 on Dirichlet point) in order to ensure that U=U_0 on Dirichlet boundary
solve the linear equation with a conjugate gradient method S_e is diagonla for derichlet point
make a relevant of the solution (Us=Um for slave/master points)

References EMM_DisplacementOperator::computeMagneticStress(), EMM_RealField::copy(), EMM_DisplacementOperator::getAccelerator(), EMM_DisplacementOperator::getSolver(), EMM_DisplacementOperator::mEquilibriumMatrix, EMM_DisplacementOperator::mUt, MATH_Solver::setMaximumIterationsNumber(), EMM_DisplacementOperator::spaceProjection(), EMM_DisplacementOperator::spaceRelevant(), and tBoolean.

Referenced by EMM_DisplacementOperator::computeEquilibriumMatrixDiagonalConditioner(), and EMM_DisplacementOperator::updateAtNextTimeStep().

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◆ computeFieldsAtTime()

tBoolean EMM_DisplacementOperator::computeFieldsAtTime	(	const tReal &	t,
		const tFlag &	order,
		const EMM_RealArray &	sigma,
		const EMM_RealField &	dM_dt0,
		const EMM_RealField &	M0
	)

virtualinherited

compute the fields of operator at time

Parameters

t	the time
order	order of integration of the fields
sigma	the magnetized weight of each cell
dM_dt0	the variation of M at time 0
M0	the magnetization field at each point at time t 0

Returns: true if the computation has succeeded.

compute fields at time from M and its first time derivative

Implements EMM_Operator.

Referenced by EMM_DisplacementOperator::setCFL().

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◆ computeMagneticStress() [1/3]

void EMM_DisplacementFEMOperator::computeMagneticStress	(	const tReal &	alpha,
		const tReal &	beta,
		const tUIndex &	nCells,
		const tDimension &	dim,
		const EMM_RealArray &	sigma,
		const tReal *	M,
		const tUIndex &	nData,
		tReal *	D
	)		const

protectedvirtual

compute the magnetic stress $S=\alpha S + \beta * div \left (\sigma^2 . \tilde \lambda^2 : ( \lambda^m : m \otimes m ) \right )$ to elastic stress S

Parameters

alpha	: multiplicator of the total stress
beta	: mustilicator of the magnetic stress
nCells	the size of the magnetism value
dim	dimension of the problem in [1,3]
sigma	weight of each cell
M	the magnetization field value
nData	number of data for the stress
D	the stress divergence in input the elastic stress , in output the total stress

$\displaystyle S_{3i_Q+d} =\alpha * S_{3i_Q+d} - \beta * \sum_{w \in V(i_Q)} \sum_{l,u,v,r,s \in \{0,1,2\}^5} \lambda^{e}_{dluv}.\lambda^m_{uvrs} \sigma_i^2 m^i_r m^i_s \int_{\omega_w} \frac{\partial \Phi_q }{\partial x_l }d\omega_w$ where $ n V(i_Q) $ is the cells connected to point at global index $ i_Q $ abd q is the local index of $iQ$ in cell $\omega_w$ .

pts={[0,0,0],[1,0,0],[0,1,0],[1,1,0],[0,0,1],[1,0,1],[0,1,1],[1,1,1]} local coordinates of cell points.
P is the number of points of the domain
- - index of the cell c
  - if iCell is in magnetized domain
    - $\lambda^e=getLambda^e(iCell)$ of size 3x3x3x3
    - $\lambda^m=getLambda^m(iCell)$ of size 3x3x3x3
    - of size 3
    - loop on nodes of cell iCell of local coordinate .
      - compute the index of the point iP=(i+Px)+Nx*(j+Py)+Nx.Ny.(k+Pz)
      - $\forall (d,l,u,v,r,s)\in R^6, \displaystyle D_{i_Q,d}=alpha * D_{i_Q,d} - beta* \sigma_i^2*\lambda^e_{kluv}.^lambda^m_{uvrs}.M_s. M_r D_{ql} . \frac{h_0.h_1.h_2}{4.h_l}$

start=iq+Px.(jq+Py.kq)

Implements EMM_DisplacementOperator.

References EMM_Grid3D::ELEMENT_POINTS, EMM_DisplacementOperator::getAdimensionizedSegmentsSize(), EMM_Operator::getElementVolume(), EMM_DisplacementOperator::getLambdaEDoubleDotLambdaM(), getNeighborsIndicator(), getPeriodicIndicator(), getPointsNumber(), CORE_Array< T >::getSize(), EMM_4Tensors::getTensorSize(), CORE_Object::getThread(), CORE_Thread::getThreadsNumber(), INT_GRAD_PHI, INT_GRAD_PHI_FACTOR, EMM_Grid3D::IS_ELEMENT_MAGNETIZED(), EMM_Tensors::isNotNull(), OMP_GET_THREAD_ID, OMP_PARALLEL_PRIVATE_SHARED_DEFAULT, EMM_Grid3D::POINTS_NUMBER_PER_ELEMENT, tBoolean, tCellFlag, tCInt, tDimension, tInteger, tReal, tUCInt, tUIndex, and tUInteger.

Referenced by EMMG_DisplacementFEMOperator::computeMagneticStress(), and getDataFieldSpace().

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◆ computeMagneticStress() [2/3]

void EMM_DisplacementOperator::computeMagneticStress	(	const EMM_RealArray &	sigma,
		const EMM_RealField &	M,
		EMM_RealField &	S
	)		const

inlineinherited

compute the magnetic stress for all cells $S=div(\lambda^e:\lambda^m:M\otimes M)$

Parameters

[in]	sigma	magnetized weight for each cell
[in]	M	the magnetization field
[out]	S	the magnetic stress dield

It computes:

$\forall (i,k) \in [0,N[\times[0,d[, S^i_k= \displaystyle div(\lambda^e:(\lambda^m:m \times m)_k = \displaystyle \sum_{l=0}^{d-1} \frac{\partial \left( \displaystyle \sum_{r,s,i,j=0}^{r,s,i,j=d-1} \lambda^e_{klij} . \lambda^m_{ijrs} m^i_r . m^i_s \right )}{\partial x_l}$ where

is the s-coordinate of the magnetization field M at cell i when s is in [0,d[ and d is the dimension of the space (i.e. 3).
is the r-coordinate of center of cell

References EMM_DisplacementOperator::computeEnergy(), EMM_RealField::setDimension(), EMM_RealField::setSize(), tDimension, tReal, and tUIndex.

Referenced by EMM_DisplacementOperator::computeEquilibriumState(), and EMM_DisplacementOperator::computeStress().

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◆ computeMagneticStress() [3/3]

virtual void EMM_DisplacementOperator::computeMagneticStress	(	const tReal &	alpha,
		const tReal &	beta,
		const EMM_RealArray &	sigma,
		const EMM_RealField &	M,
		EMM_RealField &	S
	)		const

pure virtualinherited

compute the magnetic stress for all cells from the stress $S=alpha*S+beta*div(\lambda^e:\lambda^m:M\otimes M)$

Parameters

[in]	alpha	: multiplicator factor for S
[in]	beta	: multiplicator factor for magnetic stress
[in]	sigma	the magnetized weight of cells
[in]	M	the magnetization field
[in,out]	S	the total stress field

It computes:

$\forall (i,k) \in [0,N[\times[0,d[, S^i_k= \alpha S^i_k +\displaystyle \beta. div(\lambda^e:(\lambda^m:m \times m)_k = \alpha S^i_k + \displaystyle \beta . \sum_{l=0}^{d-1} \frac{\partial \left( \displaystyle \sum_{r,s,i,j=0}^{r,s,i,j=d-1} \lambda^e_{klij} . \lambda^m_{ijrs} m^i_r . m^i_s \right )}{\partial x_l}$ where

is the s-coordinate of the magnetization field M at cell i when s is in [0,d[ and d is the dimension of the space (i.e. 3).
is the r-coordinate of center of cell

Implemented in EMMG_DisplacementFVM_VOGGROperator, EMMG_DisplacementFVM_SSGROperator, EMMG_DisplacementFVM_STEGROperator, EMMG_DisplacementFVM_VTEGROperator, and EMMG_DisplacementFEMOperator.

◆ computePotentialEnergy()

tReal EMM_DisplacementFEMOperator::computePotentialEnergy ( const EMM_RealField & U ) const

virtual

compute the potential energy to the space variation of the displacement

Parameters

U	displacement field

Returns: potential energy value $\int_\omega (\lambda^e:\varepsilon(u)):\varepsilon(u) d\omega$

Reimplemented from EMM_DisplacementOperator.

References EMM_DisplacementOperator::computePotentialEnergy().

Referenced by getDataFieldSpace().

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◆ computePotentialEnergyAtTime()

tReal EMM_DisplacementOperator::computePotentialEnergyAtTime ( const tReal & t ) const

inlineinherited

compute the potential energy to the space variation of the displacement

Parameters

t	time in [0,dt[ where dt is the time step

Returns: potential energy value $\int_\omega (\lambda^e:\varepsilon(u)):\varepsilon(u) d\omega$

References EMM_DisplacementOperator::computePotentialEnergy(), EMM_DisplacementOperator::getDisplacement(), and tReal.

Referenced by EMM_DisplacementOperator::computeEnergy().

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◆ computeStress()

void EMM_DisplacementOperator::computeStress	(	const EMM_RealArray &	sigma,
		const EMM_RealField &	U,
		const EMM_RealField &	M,
		EMM_RealField &	stress
	)		const

inlineinherited

compute the stress $div(sigma(U,M))=div(\lambda^e:\epsilon(U))-div(\lambda^2:\lambda^m:M\otimes M)$

Parameters

sigma	magnetized weight for each cell
U	the displacement field
M	the magnetization field
stress	the divergence stress field

It calls:

EMM_DisplacementOPerator::computeElasticStress();
EMM_DisplacementOperator::computeMagneticStress();

References EMM_DisplacementOperator::computeElasticStress(), and EMM_DisplacementOperator::computeMagneticStress().

Referenced by EMM_DisplacementOperator::computeFieldsAtTimeWithGLnInterpolation(), EMM_DisplacementOperator::restore(), and EMM_DisplacementOperator::updateAtNextTimeStep().

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◆ computeStressConstraintEnergy() [1/2]

tReal EMM_DisplacementFEMOperator::computeStressConstraintEnergy ( const EMM_RealField & Uf ) const

virtual

compute the stress constraint energy on boundary

Parameters

Uf	the displacement field whose Slave point are set from its master point value

Returns: the corresponding energy $\int_{partial \omega} C.U d\sigma$

periodicity of the domain

Implements EMM_DisplacementOperator.

References EMM_Grid3D::ELEMENT_POINTS, EMM_Grid3D::FACE_POINTS, EMM_DisplacementOperator::getAdimensionizedSegmentsSize(), EMM_DisplacementOperator::getConstraints(), EMM_RealField::getDimension(), EMM_DisplacementOperator::getLimitConditionOnPoints(), getNeighborsIndicator(), getPeriodicIndicator(), getPointsNumber(), CORE_Array< T >::getSize(), CORE_Object::getThread(), CORE_Thread::getThreadsNumber(), EMM_RealField::getValues(), iand, EMM_Grid3D::IS_ELEMENT_MAGNETIZED(), EMM_Grid3D::isFaceOnNeumannBoundary(), null, OMP_GET_THREAD_ID, OMP_PARALLEL_PRIVATE_SHARED_DEFAULT_REDUCTION, EMM_Grid3D::POINTS_NUMBER_PER_FACE, tBoolean, tCellFlag, tDimension, tLimitCondition, tReal, tUCInt, tUIndex, and tUInteger.

Referenced by getDataFieldSpace().

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◆ computeStressConstraintEnergy() [2/2]

tReal EMM_DisplacementOperator::computeStressConstraintEnergy ( const tReal & t ) const

inlineinherited

compute the energy of the boundary stress constraint

Parameters

t	time in [0,dt[ where dt is the time step

References EMM_DisplacementOperator::getDisplacement(), and tReal.

Referenced by EMM_DisplacementOperator::computeEnergy().

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◆ discretize()

tBoolean EMM_DisplacementFEMOperator::discretize ( const EMM_LandauLifschitzSystem & system )

virtual

discretize the operator

Parameters

system the data to discretize the operator

Returns: true if it succeeds

call EMM_DisplacementOperator::discretize()
create the mass matrix
compute the accelerator vector at t=0

compute the accelerator and the first time field

Reimplemented from EMM_DisplacementOperator.

References EMM_DisplacementOperator::discretize(), EMM_DisplacementOperator::getAccelerator(), EMM_DisplacementOperator::getDisplacement(), EMM_DisplacementOperator::getLimitConditionOnPointsByReference(), EMM_LandauLifschitzSystem::getMagnetizationField(), EMM_LandauLifschitzSystem::getMesh(), EMM_LandauLifschitzSystem::getSigma(), EMM_DisplacementOperator::getVelocity(), EMM_Grid3D::getVerticesNumber(), mMassMatrix, NewMassMatrix(), CORE_Object::out(), CORE_Out::println(), EMM_RealField::setSize(), tBoolean, toString(), tUIndex, and EMM_DisplacementOperator::updateAtNextTimeStep().

Referenced by buildDataOnBoundaryFaces().

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◆ getAccelerator() [1/2]

EMM_RealField& EMM_DisplacementOperator::getAccelerator ( )

inlineinherited

get the accelerator for writing

Returns: the accelerator field

Referenced by EMM_DisplacementOperator::computeEquilibriumState(), EMM_DisplacementFVMOperator::discretize(), discretize(), EMM_DisplacementFVMOperator::getDataFieldSpace(), getDataFieldSpace(), EMM_DisplacementFVM_VIGROperator::initializeEquilibriumSolver(), and EMM_DisplacementOperator::initializeEquilibriumSolver().

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◆ getAccelerator() [2/2]

const EMM_RealField& EMM_DisplacementOperator::getAccelerator ( ) const

inlineinherited

get the accelerator for reading

Returns: the accelerator field

References EMM_DisplacementOperator::setSolver(), and tString.

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◆ getAdimensionizedSegmentsSize()

const tReal* EMM_DisplacementOperator::getAdimensionizedSegmentsSize ( ) const

inlineinherited

get the segments size in all directions

Returns: an array of size 3 which give sthe step size in the i-direction for i in [0,3[

References EMM_DisplacementOperator::mL.

Referenced by buildDataOnNeumannBoundaryFaces(), EMM_DisplacementFVMOperator::computeElasticStress(), computeElasticStress(), EMM_DisplacementFVMOperator::computeElasticTensor(), computeElasticTensor(), EMM_DisplacementFVMOperator::computeEquilibriumMatrixDiagonalConditioner(), computeEquilibriumMatrixDiagonalConditioner(), EMM_DisplacementFVMOperator::computeMagneticStress(), computeMagneticStress(), and computeStressConstraintEnergy().

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◆ getAdimensionizedVolumicMass()

const EMM_RealArray& EMM_DisplacementOperator::getAdimensionizedVolumicMass ( ) const

inlineinherited

get the adimensionized volumic mass per cell

Returns: the adimensionized volumic mass

References EMM_DisplacementOperator::mKappa.

Referenced by EMM_DisplacementFVMOperator::computeCineticEnergy(), and computeCineticEnergy().

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◆ getClassName() [1/2]

tString CORE_Object::getClassName ( ) const

inherited

return the class name of the object

Returns: the class name of the object

References tString.

Referenced by CORE_Object::getIdentityString(), EMM_Operator::getName(), and CORE_Object::isMemoryChecked().

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◆ getClassName() [2/2]

static tString CORE_Object::getClassName ( const tString & identityString )

inlinestaticinherited

return the class name of the object

Parameters

identityString the identity string of the object

Returns: the class name

◆ getConstraintFaces()

const tFlag& EMM_DisplacementOperator::getConstraintFaces ( ) const

inlineinherited

get the constraint faces $C=\sum_{f=0}^{f=5} C_f 2^f$ $ C_f=1 $ if face f is constrainted

Returns: the constraints faces

References EMM_DisplacementOperator::mConstraintFaces.

Referenced by buildDataOnNeumannBoundaryFaces(), and EMM_DisplacementFVMOperator::computeElasticStress().

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◆ getConstraints() [1/2]

const EMM_RealField& EMM_DisplacementOperator::getConstraints ( ) const

inlineinherited

get the constraints field for reading

Returns: the constraints field

Referenced by addBoundaryElasticStress(), EMM_DisplacementFVMOperator::computeElasticStress(), EMM_DisplacementOperator::computeEnergy(), and computeStressConstraintEnergy().

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◆ getConstraints() [2/2]

EMM_RealField& EMM_DisplacementOperator::getConstraints ( )

inlineinherited

get the constraints field for writing

Returns: the constraints field

◆ getDataField() [1/3]

virtual tBoolean EMM_DisplacementOperator::getDataField	(	const tUSInt &	index,
		tString &	dataName,
		tUIndex &	n,
		tDimension &	dim,
		const float *&	values
	)		const

inlinevirtualinherited

get the data field at index for saving data in vtk,txt,... files.

Parameters

index	index of the field in [0,getDataFieldsNumber()[
dataName	name of the field
n	number of element of the field
dim	dimension of the field in [1,3[
values	values of the field

Returns

true if the field at index exists

0 : it returns the displacement field U
1 : it returns the velocity field dU_dt
2 : it returns the accelerator field acc= $\frac{d^2U}{dt^2}$

Reimplemented from EMM_Operator.

References tBoolean.

◆ getDataField() [2/3]

virtual tBoolean EMM_DisplacementOperator::getDataField	(	const tUSInt &	index,
		tString &	dataName,
		tUIndex &	n,
		tDimension &	dim,
		const double *&	values
	)		const

inlinevirtualinherited

get the data field at index for saving data in vtk,txt,... files.

Parameters

index	index of the field in [0,getDataFieldsNumber()[
dataName	name of the field
n	number of element of the field
dim	dimension of the field in [1,3[
values	values of the field

Returns

true if the field at index exists

0 : it returns the displacement field U
1 : it returns the velocity field dU_dt
2 : it returns the accelerator field acc= $\frac{d^2U}{dt^2}$

Reimplemented from EMM_Operator.

References tBoolean.

◆ getDataField() [3/3]

virtual tBoolean EMM_DisplacementOperator::getDataField	(	const tUSInt &	index,
		tString &	dataName,
		tUIndex &	n,
		tDimension &	dim,
		const long double *&	values
	)		const

inlinevirtualinherited

get the data field at index for saving data in vtk,txt,... files.

Parameters

index	index of the field in [0,getDataFieldsNumber()[
dataName	name of the field
n	number of element of the field
dim	dimension of the field in [1,3[
values	values of the field

Returns

true if the field at index exists

0 : it returns the displacement field U
1 : it returns the velocity field dU_dt
2 : it returns the accelerator field acc= $\frac{d^2U}{dt^2}$

Reimplemented from EMM_Operator.

References tBoolean.

◆ getDataFieldsNumber()

virtual tUSInt EMM_DisplacementOperator::getDataFieldsNumber ( ) const

inlinevirtualinherited

get the number of field used in the operator

Returns: the number of data

Reimplemented from EMM_Operator.

References EMM_DisplacementOperator::isSteadyState().

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◆ getDataFieldSpace()

virtual tBoolean EMM_DisplacementFEMOperator::getDataFieldSpace	(	const tUSInt &	index,
		tString &	dataName,
		tFlag &	supportType,
		tString &	dFieldType,
		tUIndex &	n,
		tDimension &	dim
	)		const

inlinevirtual

get the data field at index for saving data in vtk,txt,... files.

Parameters

index	index of the field in [0,getDataFieldsNumber()[
dataName	name of the field
supportType	: mesh element whre the field is applied EMM_Grid3D::ELEMENT; \|\| EMM_Grid3D::POINT
dFieldType	: type of the field double,float,int,....
n	number of element of the field
dim	dimension of the field in [1,3[

Returns: true if the field at index exists

Reimplemented from EMM_Operator.

References addBoundaryElasticStress(), computeCineticEnergy(), computeElasticStress(), computeElasticTensor(), computeEquilibriumMatrixDiagonalConditioner(), computeMagneticStress(), computePotentialEnergy(), computeStressConstraintEnergy(), EMM_DisplacementOperator::getAccelerator(), EMM_RealField::getDimension(), EMM_DisplacementOperator::getDisplacement(), EMM_RealField::getSize(), EMM_DisplacementOperator::getVelocity(), EMM_Grid3D::POINT, solveAcceleratorSystem(), spaceProjection(), spaceRelevant(), tBoolean, tDimension, tReal, and tUIndex.

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◆ getDisplacement() [1/3]

EMM_RealField& EMM_DisplacementOperator::getDisplacement ( )

inlineinherited

get the displacement for writing

Returns: the displacement field

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◆ getDisplacement() [2/3]

const EMM_RealField& EMM_DisplacementOperator::getDisplacement ( ) const

inlineinherited

get the displacement for reading

Returns: the displacement field

◆ getDisplacement() [3/3]

const EMM_RealField& EMM_DisplacementOperator::getDisplacement ( const tReal & t ) const

inlineinherited

get the veolicty at time

Parameters

t	time to get velocity

References EMM_DisplacementOperator::isSteadyState().

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◆ getDoubleEpsilon()

static tDouble CORE_Object::getDoubleEpsilon ( )

inlinestaticinherited

get the epsilon value for tDouble type

Returns: the epsilon value for tDouble type

Referenced by CORE_Test::testType().

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◆ getDoubleInfinity()

static tDouble CORE_Object::getDoubleInfinity ( )

inlinestaticinherited

get the infinity value for tFloat type

Returns: the intinity value for tFloat type

◆ getElasticTensor()

const EMM_2PackedSymmetricTensors& EMM_DisplacementOperator::getElasticTensor ( ) const

inlineinherited

return the elastic tensor $\varepsilon(u)=\displaystyle \frac{1}{2} \left ( \frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i} \right )$

Returns: the aelastic tensor

References EMM_DisplacementOperator::mEpsilonUt.

Referenced by EMM_DisplacementOperator::computeEnergy().

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◆ getElementVolume()

const tReal& EMM_Operator::getElementVolume ( ) const

inlineinherited

return the adimensionized volume of the element

Returns: the voume of the element with adimensionized dimensions

References EMM_Operator::mElementVolume.

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◆ getEpsilon()

template<class T >

static T CORE_Object::getEpsilon ( )

inlinestaticinherited

get the epsilon value for T type

Returns: the epsilon value for T type

◆ getFloatEpsilon()

static tFloat CORE_Object::getFloatEpsilon ( )

inlinestaticinherited

get the epsilon value for tFloat type

Returns: the epsilon value for tFloat type

Referenced by CORE_Test::testType().

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◆ getFloatInfinity()

static tFloat CORE_Object::getFloatInfinity ( )

inlinestaticinherited

get the infinity value for tFloat type

Returns: the intinity value for tFloat type

◆ getIdentityString()

tString CORE_Object::getIdentityString ( ) const

inlineinherited

return the identity string of the object of the form className_at_address

Returns: the identity string of the object

References CORE_Object::getClassName(), CORE_Object::pointer2String(), and tString.

Referenced by MATH_GaussLegendreIntegration::copy(), EMM_MultiScaleGrid::initialize(), CORE_Object::isInstanceOf(), CORE_Object::printObjectsInMemory(), MATH_Matrix::toString(), EMMG_SLPeriodicMultiScale::toString(), EMM_Stepper::toString(), EMM_AnisotropyDirectionsField::toString(), EMM_BlockMassMatrix::toString(), CORE_Object::toString(), EMM_Tensors::toString(), EMM_MultiScaleGrid::toString(), EMM_MatterField::toString(), EMM_Grid3D::toString(), and EMM_LandauLifschitzSystem::toString().

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◆ getInfinity()

template<class T >

static T CORE_Object::getInfinity ( )

inlinestaticinherited

get the infinity for T type

Returns: the infinity value for T type

◆ getLambdaE()

const EMM_4SymmetricTensors& EMM_DisplacementOperator::getLambdaE ( ) const

inlineinherited

return the adimensionized elastic tensor distribution $\lambda^e$

Returns: the adimensionized elastic tensor of size 3x3x3x3 at each cell of size nCells in a morse array

Referenced by EMM_DisplacementFVMOperator::computeElasticStress(), computeElasticStress(), EMM_DisplacementFVMOperator::computeEquilibriumMatrixDiagonalConditioner(), and computeEquilibriumMatrixDiagonalConditioner().

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◆ getLambdaEDoubleDotLambdaM()

const EMM_4Tensors& EMM_DisplacementOperator::getLambdaEDoubleDotLambdaM ( ) const

inlineinherited

return the adimensionized magnetic tensor distribution $\lambda^e:\lambda^m$

Returns: the adimensionized magnetic tensor of size 3x3x3x3 at each cell of size nCells in a morse array

Referenced by EMM_DisplacementFVMOperator::computeMagneticStress(), and computeMagneticStress().

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◆ getLambdaMDoubleDotLambdaE()

const EMM_4Tensors& EMM_DisplacementOperator::getLambdaMDoubleDotLambdaE ( ) const

inlineinherited

return the adimensionized magnetic tensor distribution $\lambda^m:\lambda^e$

Returns: the adimensionized magnetic tensor of size 3x3x3x3 at each cell of size nCells in a morse array

◆ getLambdaMDoubleDotLambdaEDoubleDotLambdaM()

const EMM_4SymmetricTensors& EMM_DisplacementOperator::getLambdaMDoubleDotLambdaEDoubleDotLambdaM ( ) const

inlineinherited

return the adimensionized magnetic tensor distribution $\lambda^m:\lambda^e:\lambda^m$

Returns: the adimensionized magnetic tensor of size 3x3x3x3 at each cell of size nCells in a morse array

Referenced by EMM_MagnetostrictionOperator::computeEnergy().

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◆ getLDoubleEpsilon()

static tLDouble CORE_Object::getLDoubleEpsilon ( )

inlinestaticinherited

get the epsilon value for tLDouble type

Returns: the epsilon value for tLDouble type

Referenced by CORE_Test::testType().

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◆ getLDoubleInfinity()

static tDouble CORE_Object::getLDoubleInfinity ( )

inlinestaticinherited

get the infinity value for tDouble type

Returns: the infinity value for tDouble type

◆ getLimitConditionOnPoints()

const EMM_LimitConditionArray& EMM_DisplacementOperator::getLimitConditionOnPoints ( ) const

inlineinherited

References CORE_Array< T >::get().

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◆ getLimitConditionOnPointsByReference()

SPC::EMM_LimitConditionArray EMM_DisplacementOperator::getLimitConditionOnPointsByReference ( ) const

inlineinherited

Referenced by discretize().

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◆ getMassMatrixType()

const tFlag& EMM_DisplacementFEMOperator::getMassMatrixType ( ) const

inline

get the mass matrix type

Returns: the mass matrix type CANONICAL,BLOCK,CONDENSED

References mMassMatrixType, and NewMassMatrix().

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◆ getMaxChar()

static tChar CORE_Object::getMaxChar ( )

inlinestaticinherited

get the max value for tChar type

Returns: the max value for tChar type

Referenced by CORE_Test::testType().

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◆ getMaxDouble()

static tDouble CORE_Object::getMaxDouble ( )

inlinestaticinherited

get the max value for tDouble type

Returns: the max value for tDouble type

Referenced by CORE_Test::testType().

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◆ getMaxFlag()

static tFlag CORE_Object::getMaxFlag ( )

inlinestaticinherited

get the max value for the tFlag type

Returns: the max value for the tFlag type

Referenced by CORE_Test::testType().

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◆ getMaxFloat()

static tFloat CORE_Object::getMaxFloat ( )

inlinestaticinherited

get the max value for tFloat type

Returns: the max value for tFloat type

Referenced by CORE_Test::testType().

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◆ getMaxIndex()

static tIndex CORE_Object::getMaxIndex ( )

inlinestaticinherited

get the max value for the array/vector indexing type

Returns: the max value for the array/vector indexing type

Referenced by CORE_Test::testType().

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◆ getMaxInt()

static tInt CORE_Object::getMaxInt ( )

inlinestaticinherited

get the max value for tInt type

Returns: the max value for tInt type

Referenced by MATSGN_FFT::fastFourierTransform3D_FFTW(), and CORE_Test::testType().

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◆ getMaxInteger()

static tInteger CORE_Object::getMaxInteger ( )

inlinestaticinherited

get the max value for the integer type

Returns: the max value for the integer type

Referenced by CORE_Test::testType().

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◆ getMaxLDouble()

static tLDouble CORE_Object::getMaxLDouble ( )

inlinestaticinherited

get the max value for tLDouble type

Returns: the max value for tLDouble type

Referenced by CORE_Test::testType().

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◆ getMaxLInt()

static tLInt CORE_Object::getMaxLInt ( )

inlinestaticinherited

get the max value for tLInt type

Returns: the max value for tLInt type

Referenced by CORE_Test::testType().

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◆ getMaxLLInt()

static tLLInt CORE_Object::getMaxLLInt ( )

inlinestaticinherited

get the max value for tULInt type

Returns: the max value for tULInt type

Referenced by CORE_Test::testType().

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◆ getMaxReal()

static tReal CORE_Object::getMaxReal ( )

inlinestaticinherited

get the max value for the real type

Returns: he max value for the real type

Referenced by EMM_MatterField::adimensionize(), and CORE_Test::testType().

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◆ getMaxSInt()

static tSInt CORE_Object::getMaxSInt ( )

inlinestaticinherited

get the max value for tSInt type

Returns: the max value for tSInt type

Referenced by CORE_Test::testType().

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◆ getMaxUChar()

static tUChar CORE_Object::getMaxUChar ( )

inlinestaticinherited

get the max value for tUChar type

Returns: the max value for tUChar type

Referenced by CORE_Test::testType().

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◆ getMaxUIndex()

static tUIndex CORE_Object::getMaxUIndex ( )

inlinestaticinherited

get the max value for difference the array/vector indexing type

Returns: the max value for difference the array/vector indexing type

Referenced by CORE_Vector< T >::addAfterIndices(), CORE_Vector< T >::search(), CORE_Test::testType(), CORE_Integer::toHexString(), and CORE_Integer::toString().

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◆ getMaxUInt()

static tUInt CORE_Object::getMaxUInt ( )

inlinestaticinherited

get the max value for tUInt type

Returns: the max value for tUInt type

Referenced by EMM_Array< tCellFlag >::loadFromFile(), EMM_RealField::loadFromFile(), and CORE_Test::testType().

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◆ getMaxUInteger()

static tUInteger CORE_Object::getMaxUInteger ( )

inlinestaticinherited

get the max value for the unsigned integer type

Returns: the max value for the unsigned integer type

Referenced by MATH_Pn::computeExtrenums(), EMM_MultiScaleGrid::computeLevelsNumber(), EMM_Input::restoreBackup(), MATH_P0::solve(), and CORE_Test::testType().

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◆ getMaxULInt()

static tULInt CORE_Object::getMaxULInt ( )

inlinestaticinherited

get the max value for tULInt type

Returns: the max value for tULInt type

Referenced by CORE_Test::testType().

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◆ getMaxULLInt()

static tULLInt CORE_Object::getMaxULLInt ( )

inlinestaticinherited

get the max value for tULLInt type

Returns: the max value for tULLInt type

Referenced by CORE_Test::testType().

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◆ getMaxUSInt()

static tUSInt CORE_Object::getMaxUSInt ( )

inlinestaticinherited

get the max value for tUSInt type

Returns: the max value for tUSInt type

Referenced by CORE_Test::testType().

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◆ getMemorySize()

virtual tULLInt EMM_DisplacementFEMOperator::getMemorySize ( ) const

inlinevirtual

return the memory size in byte

Returns: the memory size of the storage in bytes 1 Kb = 1024 bytes 1 Mb = 1024 Kb 1 Gb = 1024 Mb 1 Tb = 1024 Gb 1 Hb = 1024 Tb

Reimplemented from EMM_DisplacementOperator.

References EMM_DisplacementOperator::getMemorySize().

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◆ getMinChar()

static tChar CORE_Object::getMinChar ( )

inlinestaticinherited

get the min value for tChar type

Returns: the min value for tChar type

Referenced by CORE_Test::testType().

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◆ getMinDouble()

static tDouble CORE_Object::getMinDouble ( )

inlinestaticinherited

get the min value for tDouble type

Returns: the min value for tDouble type

Referenced by CORE_Test::testType().

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◆ getMinFlag()

static tFlag CORE_Object::getMinFlag ( )

inlinestaticinherited

get the min value for the tFlag type

Returns: the min value for the tFlag type

Referenced by CORE_Test::testType().

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◆ getMinFloat()

static tFloat CORE_Object::getMinFloat ( )

inlinestaticinherited

get the min value for tFloat type

Returns: the min value for tFloat type

Referenced by CORE_Test::testType().

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◆ getMinIndex()

static tIndex CORE_Object::getMinIndex ( )

inlinestaticinherited

get the min value for the array/vector indexing type

Returns: the min value for the array/vector indexing type

Referenced by CORE_Test::testType().

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◆ getMinInt()

static tInt CORE_Object::getMinInt ( )

inlinestaticinherited

get the min value for tInt type

Returns: the min value for tInt type

Referenced by CORE_Test::testType().

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◆ getMinInteger()

static tInteger CORE_Object::getMinInteger ( )

inlinestaticinherited

get the min value for the integer type

Returns: the minin value for the integer type

Referenced by CORE_Test::testType().

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◆ getMinLDouble()

static tLDouble CORE_Object::getMinLDouble ( )

inlinestaticinherited

get the min value for tLDouble type

Returns: the min value for tLDouble type

Referenced by CORE_Test::testType().

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◆ getMinLInt()

static tLInt CORE_Object::getMinLInt ( )

inlinestaticinherited

get the min value for tLInt type

Returns: the min value for tLInt type

Referenced by CORE_Test::testType().

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◆ getMinLLInt()

static tLLInt CORE_Object::getMinLLInt ( )

inlinestaticinherited

get the min value for tLLInt type

Returns: the min value for tLLInt type

Referenced by CORE_Test::testType().

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◆ getMinReal()

static tReal CORE_Object::getMinReal ( )

inlinestaticinherited

get the min value for the real type

Returns: the min value for the real type

Referenced by CORE_Test::testType().

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◆ getMinSInt()

static tSInt CORE_Object::getMinSInt ( )

inlinestaticinherited

get the min value for tSInt type

Returns: the min value for tSInt type

Referenced by CORE_Test::testType().

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◆ getMinUChar()

static tUChar CORE_Object::getMinUChar ( )

inlinestaticinherited

get the min value for tUChar type

Returns: the min value for tUChar type

Referenced by CORE_Test::testType().

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◆ getMinUIndex()

static tUIndex CORE_Object::getMinUIndex ( )

inlinestaticinherited

get the min value for difference the array/vector indexing type

Returns: the min value for difference the array/vector indexing type

Referenced by CORE_Test::testType().

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◆ getMinUInt()

static tUInt CORE_Object::getMinUInt ( )

inlinestaticinherited

get the min value for tUInt type

Returns: the min value for tUInt type

Referenced by CORE_Test::testType().

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◆ getMinUInteger()

static tUInteger CORE_Object::getMinUInteger ( )

inlinestaticinherited

get the min value for the unsigned integer type

Returns: the min value for the unsigned integer type

Referenced by CORE_Test::testType().

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◆ getMinULInt()

static tULInt CORE_Object::getMinULInt ( )

inlinestaticinherited

get the min value for tULInt type

Returns: the min value for tULInt type

Referenced by CORE_Test::testType().

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◆ getMinULLInt()

static tULLInt CORE_Object::getMinULLInt ( )

inlinestaticinherited

get the min value for tULLInt type

Returns: the min value for tULLInt type

Referenced by CORE_Test::testType().

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◆ getMinUSInt()

static tUSInt CORE_Object::getMinUSInt ( )

inlinestaticinherited

get the min value for tUSInt type

Returns: the min value for tUSInt type

Referenced by CORE_Test::testType().

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◆ getName()

virtual tString EMM_Operator::getName ( ) const

inlinevirtualinherited

return an human reading name of the operator

Returns: the name of the operator

References CORE_Object::getClassName(), EMM_Operator::isAffine(), EMM_Operator::isGradientComputationable(), tBoolean, tString, and tUIndex.

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◆ getNeighborsIndicator()

const EMM_CellFlagArray& EMM_DisplacementFEMOperator::getNeighborsIndicator ( ) const

inline

return the neighbors indicator in bits $\displaystyle \sum_{f=0}^{f=F-1} v_f 2^f$ where F is the number of faces per element and $ v_f $ is 1 if there is a neighbor cell with the face f

Referenced by computeElasticStress(), computeElasticTensor(), computeEquilibriumMatrixDiagonalConditioner(), computeMagneticStress(), and computeStressConstraintEnergy().

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◆ getOut()

static SP::CORE_Out CORE_Object::getOut ( )

inlinestaticinherited

get the output

Returns: the shared pointer to the output stream

References CORE_Object::OUT.

◆ getPeriodicIndicator()

const tCellFlag& EMM_DisplacementFEMOperator::getPeriodicIndicator ( ) const

inline

get the periodicity indication

Returns: the periodicity indicator in bits: $\displaystyle \sum_{f=0}^{f=F-1} v_f 2^f$ where F is the number of faces per element and is 1 if there is a periodiity in the face f

Referenced by computeElasticStress(), computeEquilibriumMatrixDiagonalConditioner(), computeMagneticStress(), computeStressConstraintEnergy(), and spaceRelevant().

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◆ getPointerAddress()

tString CORE_Object::getPointerAddress ( ) const

inlineinherited

return the identity string of the object

Returns: the identity string of the object

References CORE_Object::pointer2String().

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◆ getPointsNumber()

const tUIndex* EMM_DisplacementFEMOperator::getPointsNumber ( ) const

inline

get the points number in each direction

Returns: the array containing the points number of size 3

Referenced by computeElasticStress(), computeElasticTensor(), computeEquilibriumMatrixDiagonalConditioner(), computeMagneticStress(), and computeStressConstraintEnergy().

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◆ getRealEpsilon()

static tReal CORE_Object::getRealEpsilon ( )

inlinestaticinherited

get the eps which is the difference between 1 and the least value greater than 1 that is representable.

Returns: the eps which is the difference between 1 and the least value greater than 1 that is representable.

Referenced by MATH_P4::solveP4De(), and CORE_Test::testType().

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◆ getRealInfinity()

static tReal CORE_Object::getRealInfinity ( )

inlinestaticinherited

get the infinity value

Returns: the inifinity value for the real type

Referenced by BrentFunction::BrentFunction(), EMM_OperatorsTest::compareDiscretizedData(), EMM_IterativeTimeStep::EMM_IterativeTimeStep(), EMM_SLElementaryDemagnetizedMatrix::Kxy(), NRFunction::NRFunction(), EMM_PolynomialInterpolationTimeStep::optimizeTimeFunction(), and CORE_Test::testType().

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◆ getSharedPointer() [1/2]

void CORE_Object::getSharedPointer ( SP::CORE_Object & p )

inlineinherited

get the shared pointer of this class into p

Parameters

p	: shared pointer of the class This

Referenced by CORE_Map< Key, Value >::getSharedPointer(), CORE_ArrayList< tString >::getSharedPointer(), EMM_Array< tCellFlag >::getSharedPointer(), CORE_Array< tCellFlag >::getSharedPointer(), CORE_MorseArray< tUChar >::getSharedPointer(), CORE_Vector< T >::getSharedPointer(), and CORE_Object::printObjectsInMemory().

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◆ getSharedPointer() [2/2]

void CORE_Object::getSharedPointer ( SPC::CORE_Object & p ) const

inlineinherited

get the shared pointer of this class into p

Parameters

p	: shared pointer of the class This

◆ getSolver()

MATH_Solver* EMM_DisplacementOperator::getSolver ( )

inlineinherited

get the solver of the system

Returns: the solver null by default

Referenced by EMM_DisplacementOperator::computeEquilibriumState(), EMMG_ClassFactory::NewInstance(), and solveAcceleratorSystem().

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◆ getThread()

static CORE_Thread& CORE_Object::getThread ( )

inlinestaticinherited

get the profilier

Returns: the profiler

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◆ getTimeIntegrationMethod()

const tFlag& EMM_DisplacementOperator::getTimeIntegrationMethod ( ) const

inlineinherited

get the time integration method for next time step

Returns: integration method in P1 | TE

References EMM_DisplacementOperator::mTimeIntegrationMethod.

◆ getTimeIntegrationOrder()

const tUCInt& EMM_DisplacementOperator::getTimeIntegrationOrder ( ) const

inlineinherited

get the time integration order for new field

Returns: integration order in {1,2}

References EMM_DisplacementOperator::mTimeIntegrationOrder.

◆ getTimeStep()

const tReal& EMM_DisplacementOperator::getTimeStep ( ) const

inlineinherited

get the time step for elasticty

Returns: the time step for elasticity

References EMM_DisplacementOperator::mDt.

◆ getTypeName()

template<class T >

static tString CORE_Object::getTypeName ( )

inlinestaticinherited

get type name

Returns: the type name of the class

References tString.

◆ getVelocity() [1/3]

EMM_RealField& EMM_DisplacementOperator::getVelocity ( )

inlineinherited

get the velocity for writing

Returns: the velocity field

Referenced by EMM_DisplacementOperator::computeCineticEnergyAtTime(), EMM_DisplacementFVMOperator::discretize(), discretize(), EMM_DisplacementFVMOperator::getDataFieldSpace(), getDataFieldSpace(), EMM_DisplacementFVMOperator::resetToInitialState(), and EMM_DisplacementOperator::resetToInitialState().

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◆ getVelocity() [2/3]

const EMM_RealField& EMM_DisplacementOperator::getVelocity ( const tReal & t ) const

inlineinherited

get the velocity at time

Parameters

t	time to get velocity

References EMM_DisplacementOperator::isSteadyState().

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◆ getVelocity() [3/3]

const EMM_RealField& EMM_DisplacementOperator::getVelocity ( ) const

inlineinherited

get the velocity at t for reading

Returns: the velocity field

◆ initializeEquilibriumSolver()

void EMM_DisplacementOperator::initializeEquilibriumSolver ( const EMM_RealField & U0 )

protectedvirtualinherited

initialize the equilibrium solver

Parameters

[in] U0 is the value of U on dirichlet points

create the equilibrium matrix
compute the preconditioner matrix
compute the constant part of the affine elastic stree operator and store it in accelerator field

Reimplemented in EMM_DisplacementFVM_VIGROperator.

References EMM_DisplacementOperator::computeElasticStress(), EMM_DisplacementOperator::getAccelerator(), EMM_RealField::getDimension(), EMM_DisplacementOperator::getDisplacement(), EMM_RealField::getSize(), EMM_RealField::getValues(), EMM_RealField::initField(), EMM_DisplacementOperator::mEquilibriumMatrix, EMM_DisplacementOperator::NewEquilibriumMatrix(), EMM_RealField::NewInstance(), EMM_RealField::setDimension(), EMM_RealField::setSize(), EMM_DisplacementOperator::spaceProjection(), EMM_DisplacementOperator::spaceRelevant(), tDimension, tReal, tUIndex, and EMM_Object::Z.

Referenced by EMM_DisplacementOperator::computeEquilibriumMatrixDiagonalConditioner(), EMM_DisplacementFVM_VIGROperator::initializeEquilibriumSolver(), EMM_DisplacementOperator::restore(), and EMM_DisplacementOperator::updateAtNextTimeStep().

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◆ is32Architecture()

static tBoolean CORE_Object::is32Architecture ( )

inlinestaticinherited

return true if the machine is a 32 bits machine

Returns: true is the computing is done in a 32 bits machine

References CORE_Object::pointer2String(), CORE_Object::printObjectsInMemory(), and tString.

Referenced by CORE_Test::testType().

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◆ is64Architecture()

static tBoolean CORE_Object::is64Architecture ( )

inlinestaticinherited

return true if the machine is a 64 bits machine

Returns: true is the computing is done in a 64 bits machine

Referenced by EMM_VTK::getVTKType(), and CORE_Test::testType().

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◆ isAffine()

virtual tBoolean EMM_DisplacementOperator::isAffine ( ) const

inlinevirtualinherited

return true if the operator is either constant or linear

Returns: true if the operator is either constant or linear

Implements EMM_Operator.

◆ isCubicVolume()

const tBoolean& EMM_Operator::isCubicVolume ( ) const

inlineinherited

return the true if the element is cubic

Returns: true is all size of the volum is same

References EMM_Operator::mIsCubic.

Referenced by EMM_FullExchangeOperator::discretize(), and EMM_MinimalExchangeOperator::discretize().

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◆ isEquilibriumMatrixReconditioned()

const tBoolean& EMM_DisplacementOperator::isEquilibriumMatrixReconditioned ( ) const

inlineinherited

get if the equilibrium matrix is conditioned

Returns: true to recondition the equilibrium matrix

References EMM_DisplacementOperator::mIsEquilibriumMatrixConditioned.

Referenced by EMM_DisplacementFVMOperator::computeEquilibriumMatrixDiagonalConditioner(), and computeEquilibriumMatrixDiagonalConditioner().

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◆ isEquilibriumState()

tBoolean EMM_DisplacementOperator::isEquilibriumState ( ) const

inlineinherited

Referenced by EMM_DisplacementOperator::backup(), EMM_DisplacementOperator::computeEnergy(), EMM_DisplacementOperator::resetToInitialState(), EMM_DisplacementOperator::restore(), and EMM_DisplacementOperator::updateAtNextTimeStep().

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◆ isFrozenState()

tBoolean EMM_DisplacementOperator::isFrozenState ( ) const

inlineinherited

Referenced by EMM_DisplacementOperator::backup(), and EMM_DisplacementOperator::updateAtNextTimeStep().

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◆ isGradientComputationable()

virtual tBoolean EMM_DisplacementOperator::isGradientComputationable ( ) const

inlinevirtualinherited

return true if the gradient of the magnetic excitation is computationable

Returns: true if the the gradient of the magnetic excitation is computationable

Implements EMM_Operator.

◆ isInstanceOf() [1/2]

template<class T >

tBoolean CORE_Object::isInstanceOf ( ) const

inlineinherited

test if the clas T is an instance of this class

Returns: true if the object is an instance of T

References null.

Referenced by MATH_ToeplitzTest::toeplitzTest().

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◆ isInstanceOf() [2/2]

tBoolean CORE_Object::isInstanceOf ( const tString & name ) const

inlineinherited

test if the object is an instance of className

Parameters

name	name of the class

Returns: true if the object is an instance of class Name

References CORE_Object::getIdentityString().

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◆ isMemoryChecked()

static const tBoolean& CORE_Object::isMemoryChecked ( )

inlinestaticinherited

get if the memory checking is used

Returns: true: if the memory checking is used.

References CORE_Object::getClassName(), CORE_Object::mIsMemoryTesting, and tString.

Referenced by main().

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◆ isSteadyState()

tBoolean EMM_DisplacementOperator::isSteadyState ( ) const

inlineinherited

Referenced by EMM_DisplacementOperator::computeFieldsAtTime(), EMM_DisplacementOperator::getDataFieldsNumber(), EMM_DisplacementOperator::getDisplacement(), and EMM_DisplacementOperator::getVelocity().

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◆ NewEquilibriumMatrix()

SP::EMM_BlockEquilibriumMatrix EMM_DisplacementOperator::NewEquilibriumMatrix ( ) const

virtualinherited

create the equilibrium matrix

Returns: the equilibrium matrix

References EMM_DisplacementOperator::getDisplacement(), CORE_Object::getThis(), and EMM_BlockEquilibriumMatrix::New().

Referenced by EMM_DisplacementOperator::initializeEquilibriumSolver(), and EMM_DisplacementOperator::setCFL().

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◆ NewMassMatrix()

SP::EMM_MassMatrix EMM_DisplacementFEMOperator::NewMassMatrix ( ) const

virtual

create the accelerator matrix

Returns: the accelerator matrix

References BLOCK_MASS_MATRIX, CANONICAL_MASS_MATRIX, CONDENSED_MASS_MATRIX, mMassMatrixType, EMM_BlockMassMatrix::New(), EMM_CanonicalMassMatrix::New(), and EMM_CondensedMassMatrix::New().

Referenced by discretize(), and getMassMatrixType().

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◆ nullProjectionOnDirichletBoundary() [1/2]

void EMM_DisplacementOperator::nullProjectionOnDirichletBoundary ( EMM_RealField & V ) const

inherited

project the velocity to 0 on dirichlet boundary points

Parameters

V the field

set V=0 on Dirichlet points; V must be defined on points (return an exception if not)

References EMM_RealField::getDimension(), EMM_RealField::getValues(), EMM_RealField::initField(), EMM_DisplacementOperator::mLimitConditionOnPoints, tDimension, tReal, and tUIndex.

Referenced by EMM_DisplacementOperator::getLimitConditionOnPointsByReference(), EMM_DisplacementOperator::projectionOnDirichletBoundary(), EMM_DisplacementOperator::resetToInitialState(), and spaceProjection().

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◆ nullProjectionOnDirichletBoundary() [2/2]

void EMM_DisplacementOperator::nullProjectionOnDirichletBoundary	(	const tUIndex &	nPoints,
		const tDimension &	dim,
		tReal *	V
	)		const

inherited

project the velocity to 0 on dirichlet boundary points

Parameters

[in]	nPoints	: the number of points
[in]	dim	: the dimension of each point
[in,out]	V	: the values field defined on points

set V=0 on Dirichlet points; V must be defined on points (return an excepion if not)

References EMM_Grid3D::DIRICHLET_LIMIT_CONDITION, EMM_DisplacementOperator::getLimitConditionOnPoints(), CORE_Object::getThread(), CORE_Thread::getThreadsNumber(), OMP_GET_THREAD_ID, OMP_PARALLEL_PRIVATE_SHARED_DEFAULT, tLimitCondition, tReal, tUIndex, and tUInteger.

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◆ out()

static CORE_Out& CORE_Object::out ( )

inlinestaticinherited

get the output

Returns: the output stream

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◆ periodicProjection()

void EMM_DisplacementOperator::periodicProjection	(	const tCellFlag &	periodicity,
		const tUInteger	nPoints[3],
		EMM_RealField &	V
	)		const

inherited

make the periodic projection of the field V

Parameters

periodicity	:: periodcidcity projection
nPoints	number of points of each direction
V	field to project

V at slave point is set to V at master point

References EMM_Grid3D::GET_MASTER_PERIODIC_POINT(), EMM_RealField::getDimension(), EMM_DisplacementOperator::getLimitConditionOnPoints(), CORE_Object::getThread(), CORE_Thread::getThreadsNumber(), EMM_RealField::getValues(), null, OMP_GET_THREAD_ID, OMP_PARALLEL_PRIVATE_SHARED_DEFAULT, EMM_Grid3D::SLAVE_LIMIT_CONDITION, tDimension, tLimitCondition, CORE_Integer::toString(), tReal, tUIndex, and tUInteger.

Referenced by EMM_DisplacementOperator::getLimitConditionOnPointsByReference(), EMM_DisplacementOperator::resetToInitialState(), and spaceRelevant().

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◆ pointer2String()

tString CORE_Object::pointer2String ( const void * obj )

staticinherited

return the string representation of a pointer

Parameters

obj	: oject to get the string pointer

Returns: the string pointer of the object

References tString.

Referenced by CORE_Object::CORE_Object(), CORE_Object::getIdentityString(), CORE_Object::getPointerAddress(), CORE_Object::is32Architecture(), and CORE_Object::~CORE_Object().

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◆ printObjectsInMemory() [1/2]

void CORE_Object::printObjectsInMemory ( ostream & f )

staticinherited

print object in memory

Parameters

f	: output to print the objects in memory

References CORE_Object::getIdentityString(), CORE_Object::getSharedPointer(), CORE_Object::mIsMemoryTesting, CORE_Object::mObjects, and tInteger.

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◆ printObjectsInMemory() [2/2]

static void CORE_Object::printObjectsInMemory ( )

inlinestaticinherited

print object in memory in the standart output

Referenced by CORE_Object::is32Architecture(), and main().

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◆ projectionOnDirichletBoundary() [1/2]

void EMM_DisplacementOperator::projectionOnDirichletBoundary	(	const EMM_RealField &	V0,
		EMM_RealField &	V
	)		const

inherited

project the velocity to 0 on dirichlet boundary points

Parameters

[in]	V0	the field value on dirichlet points
[out]	V	the field

set V=V0 on Dirichlet points; V must be defined on points (return an excepion if not)

References EMM_RealField::getDimension(), EMM_RealField::getSize(), EMM_RealField::getValues(), EMM_RealField::initField(), EMM_DisplacementOperator::mLimitConditionOnPoints, null, EMM_DisplacementOperator::nullProjectionOnDirichletBoundary(), tBoolean, tDimension, tReal, and tUIndex.

Referenced by EMM_DisplacementOperator::getLimitConditionOnPointsByReference(), and spaceProjection().

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◆ projectionOnDirichletBoundary() [2/2]

void EMM_DisplacementOperator::projectionOnDirichletBoundary	(	const tUIndex &	nPoints,
		const tDimension &	dim,
		const tBoolean &	incV0,
		const tReal *	V0,
		tReal *	V
	)		const

inherited

project the velocity to 0 on dirichlet boundary points

Parameters

[in]	nPoints	the number of points
[in]	dim	the dimension of each point
[in]	incV0	increment (either 0 or 1) of the values field on dirichlet points
[in]	V0	the values field on dirichlet points of size >=3
[in,out]	V	the values field defined on points

set V=V0 on Dirichlet points; V must be defined on points (return an excepion if not)

References EMM_Grid3D::DIRICHLET_LIMIT_CONDITION, EMM_DisplacementOperator::getLimitConditionOnPoints(), CORE_Object::getThread(), CORE_Thread::getThreadsNumber(), OMP_GET_THREAD_ID, OMP_PARALLEL_PRIVATE_SHARED_DEFAULT, tDimension, tLimitCondition, tReal, tUIndex, and tUInteger.

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◆ resetOut()

static void CORE_Object::resetOut ( )

inlinestaticinherited

reset the output stream

Referenced by run().

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◆ resetThread()

static void CORE_Object::resetThread ( )

inlinestaticinherited

reset the output stream

Referenced by run().

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◆ resetToInitialState()

tBoolean EMM_DisplacementFEMOperator::resetToInitialState ( const EMM_LandauLifschitzSystem & system )

virtual

reset the operator to initial state the operator

Parameters

system the data to initialize the operator

Returns

true if it succeeds

call EMM_DisplacementOperator::resetToInitialStep()
recompute the accelerator vector at time 0

Reimplemented from EMM_DisplacementOperator.

References EMM_LandauLifschitzSystem::getMagnetizationField(), EMM_LandauLifschitzSystem::getSigma(), EMM_DisplacementOperator::resetToInitialState(), tBoolean, and EMM_DisplacementOperator::updateAtNextTimeStep().

Referenced by buildDataOnBoundaryFaces().

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◆ restore()

tBoolean EMM_DisplacementOperator::restore	(	const EMM_LandauLifschitzSystem &	system,
		const tString &	prefix,
		const tString &	suffix,
		const tString &	ext
	)

virtualinherited

restore the operator data from file(s)

Parameters

system	: general data to restore the operator
prefix	: common prefix of the saving files
suffix	: common suffix of the saving files
ext	: common extension of the saving files

Returns: if the restoring of the displacament & velocity field have succeeds

It restore the state from :

the current time step in {prefix}_dt_{suffix}.{ext}
U at previous time step in {prefix}_Unm1_{suffix}.{ext}
U at current time step in {prefix}_Un_{suffix}.{ext}
V at current time step in {prefix}_Vn_{suffix}.{ext}
dV/dt at current time step in {prefix}_Acc_{suffx}.{ext}

Reimplemented from EMM_Operator.

Reimplemented in EMM_DisplacementFVMOperator.

Referenced by EMM_DisplacementOperator::getLimitConditionOnPointsByReference(), and EMM_DisplacementFVMOperator::restore().

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◆ setCFL()

void EMM_DisplacementOperator::setCFL ( const tReal & cfl )

inlineinherited

set the cfl for computing the initial time step

Parameters

cfl	initial time step

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◆ setConstraints() [1/4]

void EMM_DisplacementOperator::setConstraints	(	const tFlag &	C,
		const tString &	dataFile
	)

inlineinherited

set constraints from file defined on points

Parameters

C	constraints faces in bit : $C=\sum_{f=0}^5 C_f 2^f$ if face f is constrainted
dataFile	: file which contains the constraints field defined on points

Referenced by EMMG_ClassFactory::NewInstance().

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◆ setConstraints() [2/4]

void EMM_DisplacementOperator::setConstraints	(	const tFlag &	C,
		const tReal	data[3]
	)

inlineinherited

set constraints field

Parameters

C	constraint faces in bit : $C=\sum_{f=0}^5 C_f 2^f$ if face f is constrainted
data	: uniform data for constraints

References EMM_RealField::setValue().

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◆ setConstraints() [3/4]

void EMM_DisplacementOperator::setConstraints	(	const tFlag &	C,
		const tReal &	C0,
		const tReal &	C1,
		const tReal &	C2
	)

inlineinherited

set initial constriants field

Parameters

C	constraint faces in bit : $C=\sum_{f=0}^5 C_f 2^f$ if face f is constrainted
C0	x-coordinate of constraint
C1	y-coordinate of constraint
C2	z-coordinate of constraint

References EMM_RealField::initField().

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◆ setConstraints() [4/4]

void EMM_DisplacementOperator::setConstraints	(	const tFlag &	C,
		const EMM_RealField &	data
	)

inlineinherited

set constraints

Parameters

C	constraint faces in bit : $C=\sum_{f=0}^5 C_f 2^f$ if face f is constrainted
data	constraints field

◆ setDisplacement() [1/2]

void EMM_DisplacementOperator::setDisplacement ( const EMM_RealField & u )

inlineinherited

set the displacement field

Parameters

u	: is the displacement field defined ob points

◆ setDisplacement() [2/2]

void EMM_DisplacementOperator::setDisplacement	(	const tReal &	Ux,
		const tReal &	Uy,
		const tReal &	Uz
	)

inlineinherited

set the displacement field to an uniform vector defied on points

Parameters

Ux	uniform value of the field on the x-direction
Uy	uniform value of the field on the y-direction
Uz	uniform value of the field on the z-direction

◆ setElasticityState()

void EMM_DisplacementOperator::setElasticityState ( const tFlag & v )

inlineinherited

set the elasticity state

Parameters

v	the elasticity state eithet equilibrium \| steady \| unsteady

Referenced by EMMG_ClassFactory::NewInstance().

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◆ setInitialDisplacement() [1/4]

void EMM_DisplacementOperator::setInitialDisplacement	(	const tReal &	scale,
		const tString &	dataFile
	)

inlineinherited

set initial displacement field.

Parameters

scale	: the scale factor of the file
dataFile	: file which contains the displacement field defined on points

Referenced by EMMG_ClassFactory::NewInstance().

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◆ setInitialDisplacement() [2/4]

void EMM_DisplacementOperator::setInitialDisplacement ( const tReal data[3] )

inlineinherited

set initial displacement field

Parameters

data	: uniform data for displacement

References EMM_RealField::setValue().

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◆ setInitialDisplacement() [3/4]

void EMM_DisplacementOperator::setInitialDisplacement	(	const tReal	U0,
		const tReal &	U1,
		const tReal &	U2
	)

inlineinherited

set initial displacement field

Parameters

U0	x-coordinate of displacement
U1	y-coordinate of displacement
U2	z-coordinate of displacement

References EMM_RealField::initField().

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◆ setInitialDisplacement() [4/4]

void EMM_DisplacementOperator::setInitialDisplacement ( const EMM_RealField & data )

inlineinherited

set initial displacement field

Parameters

data	: data for displacement

◆ setInitialVelocity() [1/4]

void EMM_DisplacementOperator::setInitialVelocity	(	const tReal &	scale,
		const tString &	dataFile
	)

inlineinherited

set initial velocity field

Parameters

scale	scale of the file
dataFile	: file which contains the velocity field defined on points

Referenced by EMMG_ClassFactory::NewInstance().

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◆ setInitialVelocity() [2/4]

void EMM_DisplacementOperator::setInitialVelocity ( const EMM_RealField & data )

inlineinherited

set initial velocity field

Parameters

data	velocity field

◆ setInitialVelocity() [3/4]

void EMM_DisplacementOperator::setInitialVelocity ( const tReal data[3] )

inlineinherited

set initial velocity field

Parameters

data	: uniform data for velocity

References EMM_RealField::setValue().

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◆ setInitialVelocity() [4/4]

void EMM_DisplacementOperator::setInitialVelocity	(	const tReal &	V0,
		const tReal &	V1,
		const tReal &	V2
	)

inlineinherited

set initial velocity field

Parameters

V0	x-coordinate of velocity
V1	y-coordinate of velocity
V2	z-coordinate of velocity

References EMM_RealField::initField().

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◆ setIsEquilibriumMatrixReconditioned()

void EMM_DisplacementOperator::setIsEquilibriumMatrixReconditioned ( const tBoolean & c )

inlineinherited

set to true if the equilibrium matrix is conditioned

Parameters

c	true to recondition the equilibrium matrix

◆ setIsMemoryChecked()

static void CORE_Object::setIsMemoryChecked ( const tBoolean & v )

inlinestaticinherited

set if the memory checking is used

Parameters

v	: true to check memory

Referenced by main().

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◆ setLimitConditionOnPoints() [1/2]

void EMM_DisplacementOperator::setLimitConditionOnPoints ( const EMM_IntArray & lc )

inlineinherited

set the limit condition each point is set to

Parameters

lc	the limit condition value for all points of the mesh. Interior point are ignored (0) NO_LIMIT_CONDITION for all interior points or not magnetized point DIRICHLET_LIMIT_CONDITION for all points on Dirichlet boundary NEUMANN_LIMIT_CONDITION for all points on Neumann boundary

Referenced by EMMG_ClassFactory::NewInstance().

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◆ setLimitConditionOnPoints() [2/2]

void EMM_DisplacementOperator::setLimitConditionOnPoints ( const tLimitCondition & lc )

inlineinherited

set the limit condition to all points

Parameters

lc	the limit condition value for all points of the mesh. Interiror point are ignored (0) NO_LIMIT_CONDITION for all interior points or not magnetized point DIRICHLET_LIMIT_CONDITION for all points on Dirichlet boundary NEUMANN_LIMIT_CONDITION for all points on Neumann boundary

◆ setMassMatrixType()

void EMM_DisplacementFEMOperator::setMassMatrixType ( const tFlag & t )

inline

set the mass matrix type

Parameters

t	: the mass matrix type CANONICAL,BLOCK,CONDENSED

◆ setOut()

static void CORE_Object::setOut ( SP::CORE_Out out )

inlinestaticinherited

set the output stream

Parameters

out	: the shared pointer to the new output stream

References null.

◆ setSolver() [1/2]

void EMM_DisplacementOperator::setSolver ( const tString & solverName )

virtualinherited

set the solver

Parameters

solverName

name of the solver which can be either :

CG or
biCGStab or
empty

If empty biCGStab is used only for FVM displacement with equilibrium state

Reimplemented in EMM_DisplacementFVMOperator.

References tString.

Referenced by EMM_DisplacementOperator::getAccelerator(), EMMG_ClassFactory::NewInstance(), and EMM_DisplacementFVMOperator::setSolver().

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◆ setSolver() [2/2]

void EMM_DisplacementOperator::setSolver ( SP::MATH_Solver solver )

inlineinherited

set the solver

Parameters

solver : the solver

◆ setThis()

void CORE_Object::setThis ( SP::CORE_Object p )

inlineprotectedinherited

set this weak shared pointer called toDoAfterThis setting method

Parameters

p	: shared pointer of the class This

References CORE_Object::toDoAfterThisSetting().

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◆ setThread()

static void CORE_Object::setThread ( SP::CORE_Thread thread )

inlinestaticinherited

set the thread

Parameters

thread the shared pointer to the thread

References null.

Referenced by EMM_Run::EMM_Run(), EMM_TensorsRun::EMM_TensorsRun(), and MATH_SolverRun::MATH_SolverRun().

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◆ setTimeIntegrationMethod()

void EMM_DisplacementOperator::setTimeIntegrationMethod ( const tFlag & m )

inlineinherited

set the time integration method for new field

Parameters

m	integration method in P1 \| TE

Referenced by EMMG_ClassFactory::NewInstance().

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◆ setTimeIntegrationOrder()

void EMM_DisplacementOperator::setTimeIntegrationOrder ( const tInt & o )

inlineinherited

set the time integration order for new field

Parameters

o	integration ordre in {1,2}

Referenced by EMMG_ClassFactory::NewInstance().

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◆ setVelocity() [1/2]

void EMM_DisplacementOperator::setVelocity ( const EMM_RealField & v )

inlineinherited

set the velocity of dicplacement defined on points

Parameters

v	: is the displacement velocity field

◆ setVelocity() [2/2]

void EMM_DisplacementOperator::setVelocity	(	const tReal &	Vx,
		const tReal &	Vy,
		const tReal &	Vz
	)

inlineinherited

set the displacement velocity field to an uniform vector defined on points

Parameters

Vx	uniform value of the field on the x-direction
Vy	uniform value of the field on the y-direction
Vz	uniform value of the field on the z-direction

◆ solveAcceleratorSystem()

tBoolean EMM_DisplacementFEMOperator::solveAcceleratorSystem ( EMM_RealField & V )

protectedvirtual

solve the velocity form the accelerator matrix : M.X=V V:=X

Parameters

V	input : the total stress output : the accelerator $U^{"}$

Returns: true if the solving succeeds

M is the mass matrix

Implements EMM_DisplacementOperator.

References EMM_DisplacementOperator::getSolver(), mMassMatrix, and tBoolean.

Referenced by getDataFieldSpace().

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◆ SP_OBJECT()

EMM_DisplacementFEMOperator::SP_OBJECT ( EMM_DisplacementFEMOperator )

private

◆ spaceProjection() [1/2]

void EMM_DisplacementFEMOperator::spaceProjection ( EMM_RealField & V ) const

protectedvirtual

make the projection of the vector B into the solving linear space

Parameters

[out] V field to project in linear solving space

V is set to 0 on all dirichlet points

Implements EMM_DisplacementOperator.

References EMM_DisplacementOperator::nullProjectionOnDirichletBoundary().

Referenced by getDataFieldSpace().

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◆ spaceProjection() [2/2]

void EMM_DisplacementFEMOperator::spaceProjection	(	const EMM_RealField &	V0,
		EMM_RealField &	V
	)		const

protectedvirtual

make the projection of the vector B into the solving linear space

Parameters

[in]	V0	:orthogonal vector of the linear solving space
[out]	V	: field to project in linear solving space

V is set to V0 on all dirichlet points

Implements EMM_DisplacementOperator.

References EMM_DisplacementOperator::projectionOnDirichletBoundary().

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◆ spaceRelevant()

void EMM_DisplacementFEMOperator::spaceRelevant ( EMM_RealField & V ) const

protectedvirtual

make the rebuild of the vector V from the solving space.

Parameters

V	the vector to rebuild from the solving space

V at slave periodical point is set to the value of V at the master periodical point

Implements EMM_DisplacementOperator.

References getPeriodicIndicator(), mMassMatrix, and EMM_DisplacementOperator::periodicProjection().

Referenced by getDataFieldSpace().

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◆ toDoAfterThisSetting()

virtual void EMM_DisplacementOperator::toDoAfterThisSetting ( )

inlineprotectedvirtualinherited

method called after the setting of the shared pointer this method can only be called once.

Reimplemented from EMM_Object.

Reimplemented in EMM_DisplacementFVMOperator.

References EMM_Object::toDoAfterThisSetting().

Referenced by EMM_DisplacementFVMOperator::toDoAfterThisSetting().

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◆ toString()

virtual tString EMM_DisplacementFEMOperator::toString ( ) const

inlinevirtual

turn the martix into string

Reimplemented from EMM_DisplacementOperator.

Referenced by discretize().

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◆ updateAtNextTimeStep()

tBoolean EMM_DisplacementOperator::updateAtNextTimeStep	(	const tReal &	dt,
		const EMM_RealArray &	sigma,
		const EMM_RealField &	Mt
	)

virtualinherited

update the data of operator at next time step

Parameters

dt	the time step
sigma	the magnetized weight of each cell
Mt	the magnetization field at each point at next time step

Returns: true if the updating of the operator has succeeded if (dt==0) the function is called after discretization during the relaxation process

Implements EMM_Operator.

Referenced by EMM_DisplacementFVMOperator::discretize(), discretize(), EMM_DisplacementFVMOperator::resetToInitialState(), resetToInitialState(), EMM_DisplacementOperator::resetToInitialState(), and EMM_DisplacementOperator::setCFL().

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Member Data Documentation

◆ BLOCK_MASS_MATRIX

const tFlag EMM_DisplacementFEMOperator::BLOCK_MASS_MATRIX =1

static

mass matrix whose each element is a digonal matrixof size 3

Referenced by EMM_DisplacementFEMOperator(), and NewMassMatrix().

◆ CANONICAL_MASS_MATRIX

const tFlag EMM_DisplacementFEMOperator::CANONICAL_MASS_MATRIX =0

static

mass matrix whose each element is real

Referenced by NewMassMatrix().

◆ CONDENSED_MASS_MATRIX

const tFlag EMM_DisplacementFEMOperator::CONDENSED_MASS_MATRIX =2

static

mass matrix is diagonal

Referenced by NewMassMatrix().

◆ EQUILIBRIUM_STATE

const tFlag EMM_DisplacementOperator::EQUILIBRIUM_STATE =3

staticinherited

Referenced by EMMG_ClassFactory::NewInstance().

◆ FROZEN_STATE

const tFlag EMM_DisplacementOperator::FROZEN_STATE =1

staticinherited

Referenced by EMMG_ClassFactory::NewInstance().

◆ Gamma

const tReal EMM_Object::Gamma =-1.7e11

staticinherited

Referenced by EMM_MatterField::adimensionize(), EMM_Matter::adimensionize(), EMM_Test::createMatters(), and EMM_MatterTest::testAdimensionize().

◆ INT_GRAD_PHI

const tCInt EMM_DisplacementFEMOperator::INT_GRAD_PHI

staticprivate

Initial value:

={-1,-1,-1,
                                                         1 ,-1,-1,
                                                         -1, 1,-1,
                                                         1,  1,-1,
                                                         -1,-1, 1,
                                                         1 ,-1, 1,
                                                         -1, 1, 1,
                                                         1,  1, 1,}

Referenced by computeElasticTensor(), and computeMagneticStress().

◆ INT_GRAD_PHI_FACTOR

const tUCInt EMM_DisplacementFEMOperator::INT_GRAD_PHI_FACTOR =4

staticprivate

Referenced by computeElasticTensor(), and computeMagneticStress().

◆ mMassMatrix

SP::EMM_MassMatrix EMM_DisplacementFEMOperator::mMassMatrix

private

Referenced by computeCineticEnergy(), discretize(), solveAcceleratorSystem(), and spaceRelevant().

◆ mMassMatrixType

tFlag EMM_DisplacementFEMOperator::mMassMatrixType

private

Referenced by EMM_DisplacementFEMOperator(), getMassMatrixType(), and NewMassMatrix().

◆ Mu0

const tReal EMM_Object::Mu0 =4*M_PI*1e-07

staticinherited

Referenced by EMM_MatterField::adimensionize(), EMM_MagnetostrictionOperator::adimensionize(), EMM_Matter::adimensionize(), EMM_CubicAnisotropyOperator::ComputeMagneticExcitation(), EMM_CubicAnisotropyOperator::computeMagneticExcitationField(), EMM_CubicAnisotropyOperator::computeMagneticExcitationFieldGradient(), EMM_CubicAnisotropyOperator::ComputeMagneticExcitationGradient(), EMM_Test::createMatters(), EMM_MatterField::getElasticTensorAdimensionizedParameter(), and EMM_MatterTest::testAdimensionize().

◆ NULL_VALUE

const tReal EMM_Object::NULL_VALUE ={0,0,0}

staticinherited

◆ P1

const tFlag EMM_DisplacementOperator::P1 =1

staticinherited

Referenced by EMM_DisplacementOperator::computeFieldsAtTime(), EMMG_ClassFactory::NewInstance(), and EMM_DisplacementFieldsTest::test().

◆ TE

const tFlag EMM_DisplacementOperator::TE =0

staticinherited

Referenced by EMM_DisplacementOperator::backup(), EMM_DisplacementOperator::computeFieldsAtTime(), EMM_DisplacementOperator::EMM_DisplacementOperator(), EMMG_ClassFactory::NewInstance(), EMM_DisplacementOperator::restore(), EMM_DisplacementFieldsTest::test(), and EMM_DisplacementOperator::updateAtNextTimeStep().

◆ UNSTEADY_STATE

const tFlag EMM_DisplacementOperator::UNSTEADY_STATE =0

staticinherited

Referenced by EMM_DisplacementOperator::EMM_DisplacementOperator(), and EMMG_ClassFactory::NewInstance().

◆ X

const tDimension EMM_Object::X =0

staticinherited

Referenced by EMMG_RealField::fitToSize(), EMM_MassMatrix::getElementVolume(), EMM_CanonicalMassMatrix::isSymmetric(), EMM_BlockMassMatrix::product(), EMM_CondensedMassMatrix::product(), EMM_RealField::setValue(), EMM_BlockMassMatrix::toString(), and EMMG_RealField::wedge().

◆ Y

const tDimension EMM_Object::Y =1

staticinherited

Referenced by EMMG_SLSDXPeriodicMultiScale::computeMultiGridExcitationField(), EMMG_RealField::fitToSize(), EMM_MassMatrix::getElementVolume(), EMM_CanonicalMassMatrix::isSymmetric(), EMM_BlockMassMatrix::product(), EMM_CondensedMassMatrix::product(), EMM_RealField::setValue(), EMM_CanonicalMassMatrix::solve(), EMM_BlockMassMatrix::solve(), EMM_BlockMassMatrix::toString(), and EMMG_RealField::wedge().

◆ Z

const tDimension EMM_Object::Z =2

staticinherited

Referenced by EMM_DisplacementFVM_VIGROperator::initializeEquilibriumSolver(), and EMM_DisplacementOperator::initializeEquilibriumSolver().

The documentation for this class was generated from the following files:

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ EMM_DisplacementFEMOperator()

◆ ~EMM_DisplacementFEMOperator()

Member Function Documentation

◆ addBoundaryElasticStress()

◆ adimensionize()

◆ backup()

◆ buildDataOnBoundaryFaces()

◆ buildDataOnNeumannBoundaryFaces()

◆ computeCineticEnergy()

◆ computeCineticEnergyAtTime()

◆ computeElasticStress() [1/3]

◆ computeElasticStress() [2/3]

◆ computeElasticStress() [3/3]

◆ computeElasticStressMatrixProduct()

◆ computeElasticTensor() [1/2]

◆ computeElasticTensor() [2/2]

◆ computeEnergy()

◆ computeEpsilon()

◆ computeEquilibriumMatrixDiagonalConditioner()

◆ computeEquilibriumState()

◆ computeFieldsAtTime()

◆ computeMagneticStress() [1/3]

◆ computeMagneticStress() [2/3]

◆ computeMagneticStress() [3/3]

◆ computePotentialEnergy()

◆ computePotentialEnergyAtTime()

◆ computeStress()

◆ computeStressConstraintEnergy() [1/2]

◆ computeStressConstraintEnergy() [2/2]

◆ discretize()

◆ getAccelerator() [1/2]

◆ getAccelerator() [2/2]

◆ getAdimensionizedSegmentsSize()

◆ getAdimensionizedVolumicMass()

◆ getClassName() [1/2]

◆ getClassName() [2/2]

◆ getConstraintFaces()

◆ getConstraints() [1/2]

◆ getConstraints() [2/2]

◆ getDataField() [1/3]

◆ getDataField() [2/3]

◆ getDataField() [3/3]

◆ getDataFieldsNumber()

◆ getDataFieldSpace()

◆ getDisplacement() [1/3]

◆ getDisplacement() [2/3]

◆ getDisplacement() [3/3]

◆ getDoubleEpsilon()

◆ getDoubleInfinity()

◆ getElasticTensor()

◆ getElementVolume()

◆ getEpsilon()

◆ getFloatEpsilon()

◆ getFloatInfinity()

◆ getIdentityString()

◆ getInfinity()

◆ getLambdaE()

◆ getLambdaEDoubleDotLambdaM()

◆ getLambdaMDoubleDotLambdaE()

◆ getLambdaMDoubleDotLambdaEDoubleDotLambdaM()

◆ getLDoubleEpsilon()

◆ getLDoubleInfinity()

◆ getLimitConditionOnPoints()

◆ getLimitConditionOnPointsByReference()

◆ getMassMatrixType()

◆ getMaxChar()

◆ getMaxDouble()

◆ getMaxFlag()

◆ getMaxFloat()

◆ getMaxIndex()

◆ getMaxInt()