C++ main module for emicrom Package  1.0
Public Member Functions | Static Public Member Functions | Static Public Attributes | Protected Member Functions | Static Protected Member Functions | Private Member Functions | Private Attributes | List of all members
EMM_WaveFEMTest Class Reference

this class is a test class for testing wave equation using the Finite elements Method with two implementation of the obtained mass matrix as diagonal or not. More...

#include <EMM_WaveFEMTest.h>

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Public Member Functions

void setIsCondensedMassMatrix (const tBoolean &isCondensed)
 set true if the Mass Matrix is condensed or not More...
 
virtual tBoolean test (const CORE_Run &runner, const map< tString, tString > &options) const
 make the test More...
 
virtual tBoolean performanceTest (const CORE_Run &runner, const map< tString, tString > &options) const
 make the perfomance tests More...
 
tString searchPath (const tString &fileName) const
 set the path to find the file with name fileName More...
 
void getSearchingPaths (vector< tString > &vpaths) const
 get the path fro seaching the files More...
 
SP::EMM_Grid3D createDomain (const tBoolean periodicity[3], const tReal L[3], const tUInteger N[3]) const
 create a cubic mesh More...
 
void createMatters (EMM_MatterField &matters, const tUIndex &nMatters, const tFlag &anisotropy, const tUIndex &nCells, const tReal &Lmin, const tReal &Lmax) const
 create matters & distribution on matters More...
 
void computeMField (const tString &path, EMM_RealField &M, const tReal &initSeed) const
 compute normalized magnetization field More...
 
void computeMField (EMM_RealField &M, const tReal &initSeed) const
 compute normalized magnetization field More...
 
SP::EMM_LandauLifschitzSystem createSystem (const CORE_Run &runner, const map< tString, tString > &options) const
 create the system More...
 
tBoolean testType () const
 test type 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...
 
virtual tString toString () const
 return the string representation of the object node More...
 

Static Public Member Functions

static SP::EMM_WaveFEMTest New ()
 create a test class More...
 
static tReal compareField (const EMM_RealField &F, const EMM_RealField &G, tUIndex &indexMax)
 compare 2 fields More...
 
static tBoolean isInBox (const tReal dim[3], const tReal x[3])
 return true if x[k] is in the [0,dim[k]] for all k in [0,3[ More...
 
static SP::EMM_Grid3D createCube (const tReal dim[3], const tUInteger N[3])
 create a cube More...
 
static SP::EMM_Grid3D createBox (const tReal dim[3], const tUInteger N[3])
 create a box More...
 
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_Outout ()
 get the output More...
 
static SP::CORE_Out getOut ()
 get the output More...
 
static CORE_ThreadgetThread ()
 get the profilier More...
 
static const tBooleanisMemoryChecked ()
 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 PRIMARY_TESTS =0
 
static const tFlag ELEMENTARY_TESTS =1
 
static const tFlag CASE_TESTS =2
 
static const tFlag CASE_TEST =4
 
static const tFlag ALL_TESTS =3
 

Protected Member Functions

 EMM_WaveFEMTest (void)
 create the class More...
 
virtual ~EMM_WaveFEMTest (void)
 destroy the class More...
 
tBoolean waveTE2Propagation (const tBoolean &isForward, const tBoolean &isTXTOutput, const tString &prefix, const tBoolean &isPeriodic, const tBoolean dirichletLC[2], tReal U_0(const tReal &t), tReal U_L(const tReal &t), const tReal &C, const tReal &L, const tReal &cfl, const tUIndex nT, EMM_RealArray &U, EMM_RealArray &V) const
 compute the wave at any time from initial conditions U(0,.) and V(0,x) and from dirichlet limit conditions $ U_0(t) $ or/and $ U_L(t) $ and/or Neumann limit conditions $ \frac{\partial U}{\partial x}(0) =0 $ or/and $ \frac{\partial U}{\partial x}(L) =0 $ based on Taylor expansion of order 2 for time: $ \displaystyle \frac{\partial^2 U}{\partial t^2} = c^2. \frac{\partial^2 U}{\partial x^2} $ More...
 
virtual tBoolean waveSystemP1Propagation (const tBoolean &isTXTOutput, const tString &prefix, const tBoolean dirichletLC[2], tReal U_0(const tReal &t), tReal U_L(const tReal &t), const tReal &c, const tReal &L, const tReal &dt, const tUIndex nT, EMM_RealArray &U, EMM_RealArray &V) const
 compute the wave at any time from initial conditions U(0,.) and V(0,x) and from dirichlet limit conditions $ U(t,0)=U_0(t) $ or/and $ U(t,L)=U_L(t) $ and/or Neumann limit conditions $ \frac{\partial U}{\partial x}(0) =0 $ or/and $ \frac{\partial U}{\partial x}(L) =0 $ based on solving a system (U,V) : More...
 
virtual tBoolean waveSystemP2Propagation (const tBoolean &isTXTOutput, const tString &prefix, const tBoolean dirichletLC[2], tReal U_0(const tReal &t), tReal U_L(const tReal &t), const tReal &c, const tReal &L, const tReal &cfl, const tUIndex nT, EMM_RealArray &U, EMM_RealArray &V) const
 compute the wave at any time from initial conditions U(0,.) and V(0,x) and from dirichlet limit conditions $ U(t,0)=U_0(t) $ or/and $ U(t,L)=U_L(t)$ and/or Neumann limit conditions $ \frac{\partial U}{\partial x}(0) =0 $ or/and $ \frac{\partial U}{\partial x}(L) =0 $ based on solving a system (V,W) More...
 
virtual tBoolean sinusoidalWave () const
 
virtual tBoolean triangleWave () const
 
virtual tBoolean trianglePeriodicalWave () const
 
virtual tBoolean sharkWave () const
 
virtual tBoolean barWave () const
 
tReal computeEnergy (const tUIndex &n, const tReal &C, const tReal &dx, const tReal &dt, const tReal *U, const tReal *Ut) const
 compute the energy of the wave : $ E=\\frac{1}{2} \int_0^L \|\frac{\partial u}{\partial t}\|^2 dx + \int_0^L \|\frac{\partial u}{\partial x}\|^2 dx $ More...
 
tBoolean save (const tString &fileName, const tReal &dx, const tReal *U, const tUIndex &nPts) const
 save the displacement at time with space space of dx More...
 
tBoolean save (const tString &fileName, const tReal &dx, const tReal *U, const tReal *V, const tUIndex &nPts) const
 save the displacement at time with space space of dx More...
 
tBoolean load (const tString &optionFile, tString &path, tBoolean &isTXTOutput, tBoolean &isPeriodic, tBoolean dirichletLC[2], tReal &L, tUIndex &nPoints, tReal &Umax, tReal &C, tUIndex &nTimes, tReal &cfl) const
 load the data from txt file More...
 
tBoolean sinusoidalWave (const tString &method) const
 
tBoolean triangleWave (const tString &method) const
 
tBoolean trianglePeriodicalWave (const tString &method) const
 
tBoolean sharkWave (const tString &method) const
 
tBoolean barWave (const tString &method) const
 
void setThis (SP::CORE_Object p)
 set this weak shared pointer called toDoAfterThis setting method More...
 
virtual void toDoAfterThisSetting ()
 method called after setThis() method this method can oly be called once. More...
 

Static Protected Member Functions

static tReal null_function (const tReal &t)
 
static tReal shark_function (const tReal &t)
 
static tReal triangle_function (const tReal &L, const tReal &U, const tReal &x)
 
static tReal sinusoidal_function (const tReal &L, const tReal &U, const tReal &x)
 
static void linearPieceWise_function (const tUInteger &n, const tReal *X, const tReal *Y, const tUInteger &nEvals, const tReal *Xvalues, tReal *Yvalues)
 

Private Member Functions

 SP_OBJECT (EMM_WaveFEMTest)
 
void computeMassMatrix (const tUIndex &nPts, const tBoolean &isPeriodic, const tBoolean dirichletLC[2], MATH_FullMatrix &M) const
 compute the mass matrix More...
 
void computeCondensedMassMatrix (const tUIndex &nPts, const tBoolean &isPeriodic, const tBoolean dirichletLC[2], MATH_ArrayVector &M) const
 compute the condensed mass matrix as diagonal More...
 
void computeStressMatrix (const tUIndex &nPts, const tBoolean &isPeriodic, const tBoolean dirichletLC[2], MATH_FullMatrix &S) const
 compute the stress matrix More...
 
tBoolean computeWaveAtFirstTime (const MATH_Matrix &M, const MATH_Matrix &X, MATH_Solver &solver, const tBoolean &isPeriodic, const tBoolean dirichletLC[2], tReal U0(const tReal &t), tReal UL(const tReal &t), EMM_RealArray &Ux_0, EMM_RealArray &dU_dt0, const tReal &s, const tReal &dt, EMM_RealArray &Ux_1) const
 compute the wave U(dt,.) with Dirichlet/Neumann limit conditions More...
 
tBoolean computeWaveAtFirstTime (const MATH_ArrayVector &M, const MATH_Matrix &X, const tBoolean &isPeriodic, const tBoolean dirichletLC[2], tReal U0(const tReal &t), tReal UL(const tReal &t), EMM_RealArray &Ux_0, EMM_RealArray &dU_dt0, const tReal &s, const tReal &dt, EMM_RealArray &Ux_1) const
 compute the wave U(dt,.) with Dirichlet/Neumann limit conditions More...
 

Private Attributes

tBoolean mIsMassMatrixCondensed
 

Detailed Description

this class is a test class for testing wave equation using the Finite elements Method with two implementation of the obtained mass matrix as diagonal or not.

$ \displaystyle \frac{\partial^2 u}{\partial t^2} = c^2 . \frac{\partial^2 u}{\partial x^2} $

The aproximation of time is either

Constructor & Destructor Documentation

◆ EMM_WaveFEMTest()

EMM_WaveFEMTest::EMM_WaveFEMTest ( void  )
protected

create the class

References mIsMassMatrixCondensed.

Referenced by New().

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◆ ~EMM_WaveFEMTest()

EMM_WaveFEMTest::~EMM_WaveFEMTest ( void  )
protectedvirtual

destroy the class

Member Function Documentation

◆ barWave() [1/2]

tBoolean EMM_WaveTest::barWave ( const tString method) const
protectedinherited

◆ barWave() [2/2]

virtual tBoolean EMM_WaveFEMTest::barWave ( ) const
inlineprotectedvirtual

Implements EMM_WaveTest.

References EMM_WaveTest::barWave().

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◆ compareField()

tReal EMM_Test::compareField ( const EMM_RealField F,
const EMM_RealField G,
tUIndex indexMax 
)
staticinherited

compare 2 fields

Parameters
Fthe field to compare
Gthe secund field to compare
indexMaxthe index where the diffrenec of the norm is maximum
Returns
the max norm difference among all points

References EMM_RealField::getDimension(), EMM_RealField::getSize(), EMM_RealField::getValue(), tBoolean, tDimension, tReal, and tUIndex.

Referenced by EMM_Test::New(), and EMM_ODETest::testODE().

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◆ computeCondensedMassMatrix()

void EMM_WaveFEMTest::computeCondensedMassMatrix ( const tUIndex nPts,
const tBoolean isPeriodic,
const tBoolean  dirichletLC[2],
MATH_ArrayVector M 
) const
private

compute the condensed mass matrix as diagonal

Parameters
nPtsnumber of rows/columns of the mass matrix
isPeriodicto set if the matrix is supposed to be periodic
dirichletLC: limite conditions
Mthe mass matrix

The mass matrix corresponding to the approximation of the integration of $ \displaystyle \int_{x_{i-1}}^{x_{i+1}} \Phi_i(x) \Phi_j (x) dx = \frac{\Phi_i(0)\Phi_j(0) + \Phi_i(1)\Phi_j(1) }{2} $ where $ \Phi_i(x_j)=\delta_{i,j} $ is a basis function P1 interpolation is as follow:

$ M = \left[ {\begin{array}{cccccc} \frac{1}{2} & 0 & ... & 0 & 0 & 0 \\ 0 & 1 & 0 & ... & 0 & 0 \\ 0 & 0 & 1 & 0 && ... \\ ... & ... & ... & ...& ... & ... \\ 0 & 0 & ...& 0 & 1 & 0 \\ 0& ... & 0 & 0 & 1 & \frac{1}{2} \end{array} } \right] $

If the condition is dirichlet at point 0 then $ M_{0,0}=1. $ or/and at point L then $ M_{n-1,n-1}=1$ and 0 on other columns.

References MATH_ArrayVector::setSize(), tReal, and tUIndex.

Referenced by setIsCondensedMassMatrix(), and waveTE2Propagation().

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◆ computeEnergy()

tReal EMM_WaveTest::computeEnergy ( const tUIndex n,
const tReal C,
const tReal dx,
const tReal dt,
const tReal U,
const tReal Ut 
) const
protectedinherited

compute the energy of the wave : $ E=\\frac{1}{2} \int_0^L \|\frac{\partial u}{\partial t}\|^2 dx + \int_0^L \|\frac{\partial u}{\partial x}\|^2 dx $

Parameters
n: number of point
Ccelerity of the wave
dxspace step size
dttime step size
U: U at t
UtU at t+dt

References null, tReal, and tUIndex.

Referenced by EMM_WaveFDMTest::waveSystemP2Propagation(), EMM_WaveFDMTest::waveTE2Propagation(), and waveTE2Propagation().

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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}

◆ computeMassMatrix()

void EMM_WaveFEMTest::computeMassMatrix ( const tUIndex nPts,
const tBoolean isPeriodic,
const tBoolean  dirichletLC[2],
MATH_FullMatrix M 
) const
private

compute the mass matrix

Parameters
nPtsnumber of rows/columns of the mass matrix
isPeriodicto set if the matrix is supposed to be periodic
dirichletLC: limite conditions
Mthe mass matrix

The mass matrix corresponding to the exact integration of $ \displaystyle \int_{x_{i-1}}^{x_{i+1}} \Phi_i(x) \Phi_j (x) dx $ where $ \Phi_i(x_j)=\delta_{i,j} $ is a basis function P1 interpolation is as follow:

$ M = \left[ {\begin{array}{cccccc} \frac{1}{3} & \frac{1}{6} & ... & 0 & 0 & 0 \\ \frac{1}{6} & \frac{2}{3} & \frac{1}{6} & ... & 0 & 0 \\ 0 & \frac{1}{6} & \frac{2}{3} & \frac{1}{6} && ... \\ ... & ... & ... & ...& ... & ... \\ 0 & 0 & ...& \frac{1}{6} & \frac{2}{3} & \frac{1}{6} \\ 0& ... & 0 & 0 & \frac{1}{6} & \frac{1}{3} \end{array} } \right] $

If the condition is dirichlet at point 0 then $ M_{0,0}=1. $ or/and at point L then $ M_{n-1,n-1}=1.$, and 0 on other columns.

References MATH_FullMatrix::setSize(), MATH_FullMatrix::setValues(), tReal, and tUIndex.

Referenced by setIsCondensedMassMatrix(), and waveTE2Propagation().

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◆ computeMField() [1/2]

void EMM_Test::computeMField ( const tString path,
EMM_RealField M,
const tReal initSeed 
) const
inherited

compute normalized magnetization field

Parameters
[in]path: path to find the M file if any
[out]M: field to generate
[in]initSeed: type of initialization of the fields :
  • -1 : M=(1,0,0)
  • -2 : M=(0,1,0)
  • -3 : M=(0,0,1)
  • -4 : M=(1,1,1)
  • -5 : M=(0,1,1)
  • -6 : M=(1,1,0)
  • -7 : M=(1,0,1)
  • >=0 : it loads the file M_nCells_initSeed.txt it its exists or create a random M and try to generete in in the path whre the file is supposed to be. The field M must be sized before.

References EMM_RealField::getSize(), EMM_RealField::initField(), EMM_RealField::loadFromFile(), EMM_RealField::saveToFile(), EMM_Test::searchPath(), EMM_RealField::setSize(), EMM_RealField::setValue(), tBoolean, CORE_Real::toString(), CORE_Integer::toString(), tReal, tString, and tUIndex.

Referenced by EMM_Test::computeMField(), and EMM_Test::New().

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◆ computeMField() [2/2]

void EMM_Test::computeMField ( EMM_RealField M,
const tReal initSeed 
) const
inlineinherited

compute normalized magnetization field

Parameters
[out]M: field to generate
[in]initSeed: type of initialization of the fields :
  • -1 : M=(1,0,0)
  • -2 : M=(0,1,0)
  • -3 : M=(0,0,1)
  • -4 : M=(1,1,1)
  • -5 : M=(0,1,1)
  • -6 : M=(1,1,0)
  • -7 : M=(1,0,1)
  • >=0 : it loads the file M_nCells_initSeed.txt it its exists or create a random M and try to generete in in the path whre the file is supposed to be. The field M must be sized before.

References EMM_Test::computeMField(), and EMM_Test::createSystem().

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◆ computeStressMatrix()

void EMM_WaveFEMTest::computeStressMatrix ( const tUIndex nPts,
const tBoolean isPeriodic,
const tBoolean  dirichletLC[2],
MATH_FullMatrix S 
) const
private

compute the stress matrix

Parameters
nPtsnumber of rows/columns of the mass matrix
isPeriodicto set if the stress is supposed to be periodic
dirichletLC: limite conditions
Sthe stress matrix

The stress matrix corresponding to the exact integration of $ \displaystyle \int_{x_{i-1}}^{x_{i+1}} \frac{\partial \Phi_i(x)}{\partial x} \frac{\partial \Phi_j (x)}{\partial x} dx $ where $ \Phi_i(x_j)=\delta_{i,j} $ is a basis function P1 interpolation is as follow:

$ S = \left[ {\begin{array}{cccccc} 1 & -1 & ... & 0 & 0 & 0 \\ -1 & 2 & -1 & ... & 0 & 0 \\ 0 & -1 & 2 & -1 && ... \\ ... & ... & ... & ...& ... & ... \\ 0 & 0 & ...& -1 & 2 & -1 \\ 0& ... & 0 & 0 & -1 & 1 \end{array} } \right] $

References MATH_FullMatrix::setSize(), MATH_FullMatrix::setValues(), tReal, and tUIndex.

Referenced by setIsCondensedMassMatrix(), and waveTE2Propagation().

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◆ computeWaveAtFirstTime() [1/2]

tBoolean EMM_WaveFEMTest::computeWaveAtFirstTime ( const MATH_Matrix M,
const MATH_Matrix X,
MATH_Solver solver,
const tBoolean isPeriodic,
const tBoolean  dirichletLC[2],
tReal   U0const tReal &t,
tReal   ULconst tReal &t,
EMM_RealArray Ux_0,
EMM_RealArray dU_dt0,
const tReal s,
const tReal dt,
EMM_RealArray Ux_1 
) const
private

compute the wave U(dt,.) with Dirichlet/Neumann limit conditions

Parameters
M: mass matrix
X: displacement matrix
solver: linear solver
isPeriodicto set if the wave is supposed to be periodic
dirichletLClimit condition of dirichlet
U0: function depending on time t at x=0 if dirichlet condition
UL: function depending on time t at x=L if dirichlet condition
Ux_0: initial value of U at t=0 for all x in [0,L[
dU_dt0: initial value of velocity of U at t=0 for all x in [0,L[
sthe quantity $ c^2*dt^2/dx^2 $
dt: the time step
Ux_1: return the values of U at t=dt

$ \displaystyle \frac{\partial U}{\partial t}(t,x)=\frac{U(t+dt,x)-U(t-dt,x)}{2.dt} $ $ \displaystyle U(t-dt,x)=U(t+dt,x)-2.dt*\frac{\partial U}{\partial t}(t,x) $

$ \displaystyle \frac{\partial^2 U}{\partial t^2}= \displaystyle \frac{U(t+dt,x)+U(t-dt,x)-2.U(t,x) }{2.dt^2}$

$ \displaystyle \frac{\partial^2 U}{\partial x^2}= \displaystyle \frac{U(t,x+dx)+U(t,x-dx)-2.U(t,x) }{2.dx^2}$

$ \displaystyle \frac{\partial^2 U}{\partial t^2}= c^2 \displaystyle \frac{\partial^2 U}{\partial x^2} $

By multipliing by a basis function $ \Phi_j(x) $ and integration over the domain, we obtain the ssystem equation:

$ \displaystyle M. \frac{U(t+dt,x)+U(t-dt,x)-2.U(t,x) }{2.dt^2} = \displaystyle c^2 \frac{1}{2.dx^2} X. U $

$ \Rightarrow \displaystyle U(t+dt)= \displaystyle c^2 \frac{dt^2}{dx^2} \left ( M^{-1}. X. U \right ) +2.U(t)-U(t-dt) $

so we deduce at first step that :

$ \displaystyle U(t+dt)= \displaystyle \frac{s^2}{2} \left ( M^{-1}. X. U \right ) + dt*\frac{\partial U}{\partial t}(x,0) $ with $ s=c \frac{dt}{dx} $

References CORE_Array< T >::add(), CORE_Array< T >::getSize(), MATH_ArrayVector::New(), MATH_Matrix::product(), CORE_Array< T >::setSize(), MATH_Solver::solve(), tReal, and tUIndex.

Referenced by setIsCondensedMassMatrix(), and waveTE2Propagation().

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◆ computeWaveAtFirstTime() [2/2]

tBoolean EMM_WaveFEMTest::computeWaveAtFirstTime ( const MATH_ArrayVector M,
const MATH_Matrix X,
const tBoolean isPeriodic,
const tBoolean  dirichletLC[2],
tReal   U0const tReal &t,
tReal   ULconst tReal &t,
EMM_RealArray Ux_0,
EMM_RealArray dU_dt0,
const tReal s,
const tReal dt,
EMM_RealArray Ux_1 
) const
private

compute the wave U(dt,.) with Dirichlet/Neumann limit conditions

Parameters
M: condensed mass diagonal matrix
Xdisplacement matrix
isPeriodicto set if the wave is supposed to be periodic
dirichletLClimit condition of dirichlet
U0: function depending on time t at x=0 if dirichlet condition
UL: function depending on time t at x=L if dirichlet condition
Ux_0: initial value of U at t=0 for all x in [0,L[
dU_dt0: initial value of velocity of U at t=0 for all x in [0,L[
sthe quantity $ c^2*dt^2/dx^2 $
dt: the time step
Ux_1: return the values of U at t=dt

$ \displaystyle \frac{\partial U}{\partial t}(t,x)=\frac{U(t+dt,x)-U(t-dt,x)}{2.dt} $ $ \displaystyle U(t-dt,x)=U(t+dt,x)-2.dt*\frac{\partial U}{\partial t}(t,x) $

$ \displaystyle \frac{\partial^2 U}{\partial t^2}= \displaystyle \frac{U(t+dt,x)+U(t-dt,x)-2.U(t,x) }{2.dt^2}$

$ \displaystyle \frac{\partial^2 U}{\partial x^2}= \displaystyle \frac{U(t,x+dx)+U(t,x-dx)-2.U(t,x) }{2.dx^2}$

$ \displaystyle \frac{\partial^2 U}{\partial t^2}= c^2 \displaystyle \frac{\partial^2 U}{\partial x^2} $

By multipliing by a basis function $ \Phi_j(x) $ and integration over the domain, we obtain the ssystem equation:

$ \displaystyle M. \frac{U(t+dt,x)+U(t-dt,x)-2.U(t,x) }{2.dt^2} = \displaystyle c^2 \frac{1}{2.dx^2} X. U $

$ \Rightarrow \displaystyle U(t+dt)= \displaystyle c^2 \frac{dt^2}{dx^2} \left ( M^{-1}. X. U \right ) +2.U(t)-U(t-dt) $

so we deduce at first step that :

$ \displaystyle U(t+dt)= \displaystyle \frac{s^2}{2} \left ( M^{-1}. X. U \right ) + dt*\frac{\partial U}{\partial t}(x,0) $ with $ s=c \frac{dt}{dx} $

References CORE_Array< T >::add(), CORE_Array< T >::getSize(), MATH_ArrayVector::New(), MATH_Matrix::product(), CORE_Array< T >::setSize(), tReal, and tUIndex.

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◆ createBox()

SP::EMM_Grid3D EMM_Test::createBox ( const tReal  dim[3],
const tUInteger  N[3] 
)
staticinherited

create a box

Parameters
dimdimension of a parallelipiped box in each direction
Nnumber of discretization on each direction of the box
Returns
a share pointer to the grid 3D

References EMM_Grid3D::getNeighborsIndicators(), EMM_Test::isInBox(), EMM_Grid3D::New(), EMM_Grid3D::setSegmentsNumber(), EMM_Grid3D::setStepsSize(), tCellFlag, tReal, tUIndex, tUSInt, and EMM_Grid3D::updateMagnetizedElementsNumber().

Referenced by EMM_Grid3DTest::cellDataPointDataTest(), EMM_Test::createDomain(), and EMM_Test::New().

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◆ createCube()

SP::EMM_Grid3D EMM_Test::createCube ( const tReal  dim[3],
const tUInteger  N[3] 
)
staticinherited

create a cube

Parameters
dimdimension of a parallelipiped cube in each direction
Nnumber of discretization on each direction of the cube
Returns
a share pointer to the grid 3D

References EMM_Grid3D::getNeighborsIndicators(), EMM_Test::isInBox(), EMM_Grid3D::New(), EMM_Grid3D::setSegmentsNumber(), EMM_Grid3D::setStepsSize(), tCellFlag, tReal, tUInteger, tUSInt, and EMM_Grid3D::updateMagnetizedElementsNumber().

Referenced by EMM_Test::New(), EMM_TimeTest::testCubicAnisotropyEnergyDerivatives(), EMM_Grid3DTest::testSegment(), EMM_Grid3DTest::testThinSheet(), EMM_TimeTest::testTimeStepComputing(), and EMM_TimeTest::testZeemanEnergyDerivatives().

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◆ createDomain()

SP::EMM_Grid3D EMM_Test::createDomain ( const tBoolean  periodicity[3],
const tReal  L[3],
const tUInteger  N[3] 
) const
inherited

create a cubic mesh

Parameters
[in]periodicity: periodicity of the domain
[in]L: size of the domain
[in]N: discretization of the domain

References EMM_Test::createBox().

Referenced by EMM_DemagnetizedPeriodicalTest::HTest(), EMM_VelocitySolverTest::massMatrixTest(), EMM_VelocitySolverTest::massMatrixTrivialSolverTest(), EMM_DemagnetizedPeriodicalTest::multiSDGridScaleTest(), EMM_Test::New(), EMM_DemagnetizedPeriodicalTest::relaxationTest(), EMM_DemagnetizedPeriodicalTest::xyPeriodicalCubeSDGTest(), and EMM_DemagnetizedPeriodicalTest::xyPeriodicalSheetSDGTest().

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◆ createMatters()

void EMM_Test::createMatters ( EMM_MatterField matters,
const tUIndex nMatters,
const tFlag anisotropy,
const tUIndex nCells,
const tReal Lmin,
const tReal Lmax 
) const
inherited

create matters & distribution on matters

Parameters
[out]matters: matter field within the domain
[in]nMatters: number of matters to generate
[in]anisotropy: anisotrpy type of the matters
[in]nCells: number of cells of the mesh
[in]Lmin: min length of cells of the domain
[in]Lmax: max length of cells of the domain

References EMM_MatterField::addMatter(), EMM_MatterField::adimensionize(), EMM_MatterField::clear(), EMM_Matter::CUBIC_ANISOTROPY, EMM_Object::Gamma, EMM_Object::Mu0, EMM_Matter::New(), EMM_Matter::PLANAR_ANISOTROPY, EMM_MatterField::setSize(), tReal, tUIndex, and tUSInt.

Referenced by EMM_DemagnetizedPeriodicalTest::HTest(), EMM_DemagnetizedPeriodicalTest::multiSDGridScaleTest(), EMM_Test::New(), EMM_DemagnetizedPeriodicalTest::relaxationTest(), EMM_DemagnetizedPeriodicalTest::xyPeriodicalCubeSDGTest(), and EMM_DemagnetizedPeriodicalTest::xyPeriodicalSheetSDGTest().

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◆ createSystem()

SP::EMM_LandauLifschitzSystem EMM_Test::createSystem ( const CORE_Run runner,
const map< tString, tString > &  options 
) const
inherited

create the system

Parameters
[in]runner: runner of the program to get the class factory
[in]options: options to create the system
  • "relaxation-time-integration" = "gl"|"ggl"|"rk4"|"te"
  • "relaxation-time order"="2"|"1"
  • "relaxation-rate"="1.e-8"
Returns
the laudau lifschitz system

References CORE_String::New(), and tString.

Referenced by EMM_Test::computeMField(), EMM_DemagnetizedPeriodicalTest::HTest(), EMM_DemagnetizedPeriodicalTest::multiSDGridScaleTest(), EMM_DemagnetizedPeriodicalTest::relaxationTest(), EMM_DemagnetizedPeriodicalTest::xyPeriodicalCubeSDGTest(), and EMM_DemagnetizedPeriodicalTest::xyPeriodicalSheetSDGTest().

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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
identityStringthe identity string of the object
Returns
the class name

◆ 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

◆ 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

◆ getInfinity()

template<class T >
static T CORE_Object::getInfinity ( )
inlinestaticinherited

get the infinity for T type

Returns
the infinity value for T type

◆ 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

◆ 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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◆ 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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◆ getOut()

static SP::CORE_Out CORE_Object::getOut ( )
inlinestaticinherited

get the output

Returns
the shared pointer to the output stream

References CORE_Object::OUT.

◆ 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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◆ 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

◆ getSearchingPaths()

void EMM_Test::getSearchingPaths ( vector< tString > &  vpaths) const
inherited

◆ getSharedPointer() [1/2]

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

◆ 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

◆ getThread()

static CORE_Thread& CORE_Object::getThread ( )
inlinestaticinherited

get the profilier

Returns
the profiler

Referenced by MATH_MaskVector::add(), MATH_Vector::add(), EMM_DisplacementFEMOperator::addBoundaryElasticStress(), EMM_DisplacementFEMOperator::buildDataOnNeumannBoundaryFaces(), EMM_DisplacementFVMOperator::computeCineticEnergy(), EMM_DisplacementFVMOperator::computeElasticStress(), EMM_DisplacementFEMOperator::computeElasticStress(), EMM_DisplacementFVMOperator::computeElasticTensor(), EMM_DisplacementFEMOperator::computeElasticTensor(), EMM_StaticMagneticTensorOperator::computeEnergy(), EMM_CubicAnisotropyOperator::computeEnergy(), EMM_MagnetostrictionOperator::computeEnergy(), EMM_DisplacementOperator::computeEnergy(), EMM_AnisotropyOperator::computeEnergyWithMagneticExcitation(), EMM_DisplacementFVMOperator::computeEquilibriumMatrixDiagonalConditioner(), EMM_DisplacementFEMOperator::computeEquilibriumMatrixDiagonalConditioner(), EMM_FullExchangeOperator::computeMagneticExcitationField(), EMM_StaticMagnetostrictionOperator::computeMagneticExcitationField(), EMM_LinearAnisotropyOperator::computeMagneticExcitationField(), EMM_StaticMagneticTensorOperator::computeMagneticExcitationField(), EMM_CubicAnisotropyOperator::computeMagneticExcitationField(), EMM_MinimalExchangeOperator::computeMagneticExcitationField(), EMM_AnisotropyOperator::computeMagneticExcitationField(), EMM_MagnetostrictionOperator::computeMagneticExcitationField(), EMM_CubicAnisotropyOperator::computeMagneticExcitationFieldGradient(), EMM_AnisotropyOperator::computeMagneticExcitationFieldGradient(), EMM_DisplacementFVMOperator::computeMagneticStress(), EMM_DisplacementFEMOperator::computeMagneticStress(), EMM_OptimalTimeStep::computeOptimalTimeStep(), EMM_DisplacementFEMOperator::computeStressConstraintEnergy(), EMM_FullExchangeOperator::discretize(), EMM_MinimalExchangeOperator::discretize(), EMM_CondensedMassMatrix::discretize(), EMM_LinearAnisotropyOperator::discretize(), EMM_AnisotropyOperator::discretize(), EMM_DemagnetizedOperator::discretize(), EMMG_SLDemagnetizedOperator::discretize(), EMM_LandauLifschitzSystem::discretize(), MATH_Vector::divide(), MATH_MaskVector::dot(), MATH_Vector::dot(), EMM_4SymmetricTensors::doubleDot(), EMM_4Tensors::doubleDotCrossDoubleDotScalar(), EMM_4Tensors::doubleDotCrossProduct(), EMM_4Tensors::doubleDotCrossSquaredScalar(), EMM_4Tensors::doubleDotProduct(), MATH_Vector::init(), MATH_MaskVector::init(), EMM_LandauLifschitzODE_RK::integrateMagnetizationFieldAtTime(), EMM_DisplacementFVM_Interpolator::interpolateUAtVertices(), EMMG_SLDemagnetizedOperator::localAssembly(), EMM_DisplacementOperator::nullProjectionOnDirichletBoundary(), EMM_DisplacementOperator::periodicProjection(), EMM_2PackedSymmetricTensors::product(), EMM_CanonicalMassMatrix::product(), MATH_FullMatrix::product(), EMM_CondensedMassMatrix::product(), EMM_BlockMassMatrix::product(), MATH_MorseMatrix::product(), EMMG_SLDemagnetizedOperator::product(), EMM_DisplacementOperator::projectionOnDirichletBoundary(), EMM_LandauLifschitzSystem::resetOperatorsToInitialState(), EMM_DisplacementFVMOperator::setBoundaryFaceTypes(), FFTW_MultiDFTs::setFFT(), FFTW_MultiLevelsDFT::setFFT(), FFTW_MultiLevelsDFT::setLevels(), FFTW_MultiDFTs::setPlan(), FFTW_MultiLevelsDFT::setPlan(), EMM_CondensedMassMatrix::solve(), EMM_LandauLifschitzODE::solveODE(), EMM_4SymmetricTensors::squaredDoubleDot(), EMM_4Tensors::squaredDoubleDotCrossScalar(), EMM_4Tensors::squaredDoubleDotScalar(), EMM_CanonicalMassMatrix::symmetricDot(), EMM_CondensedMassMatrix::symmetricDot(), EMM_BlockMassMatrix::symmetricDot(), FFTW_Test::test(), MATH_SolverTest::test(), EMM_ODETest::testODE(), and EMM_Grid3D::updateLimitConditionOnPoints().

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◆ getTypeName()

template<class T >
static tString CORE_Object::getTypeName ( )
inlinestaticinherited

get type name

Returns
the type name of the class

References tString.

◆ 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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◆ isInBox()

tBoolean EMM_Test::isInBox ( const tReal  dim[3],
const tReal  x[3] 
)
staticinherited

return true if x[k] is in the [0,dim[k]] for all k in [0,3[

Parameters
dimdimension of the parallelepiped cube
xcoordinates of the point
Returns
trie if the point x is in the box

References tBoolean, and tUSInt.

Referenced by EMM_Test::createBox(), EMM_Test::createCube(), and EMM_Test::New().

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◆ 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
namename 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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◆ linearPieceWise_function()

void EMM_WaveTest::linearPieceWise_function ( const tUInteger n,
const tReal X,
const tReal Y,
const tUInteger nEvals,
const tReal Xvalues,
tReal Yvalues 
)
staticprotectedinherited

References tReal, and tUInteger.

Referenced by EMM_WaveTest::barWave(), EMM_WaveTest::shark_function(), and EMM_WaveTest::triangle_function().

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◆ load()

tBoolean EMM_WaveTest::load ( const tString optionFile,
tString path,
tBoolean isTXTOutput,
tBoolean isPeriodic,
tBoolean  dirichletLC[2],
tReal L,
tUIndex nPoints,
tReal Umax,
tReal C,
tUIndex nTimes,
tReal cfl 
) const
protectedinherited

load the data from txt file

Parameters
optionFilename of the file containing lines key=value The keys are
  • "dirichlet0"
  • "dirichlet1"
  • "L"
  • "nPoints"
  • "Umax"
  • "C"
  • "nTimes"
  • "cfl"
  • "txt-output"
paththe path where the option file is found
isTXTOutput: true to save the evolution in txt files
isPeriodic: true if the domain is supposed to be periodic
dirichletLC: read the dirichlet conditions on x=0 and x=L
Lthe length of the 1D-domain
nPoints: number of discretized points on x
Umaxthe maximum amplitude of U
Cthe celerity of the wave
nTimesthe number of time steps
cflthe cfl condition <=1
Returns
true if the loading succeeded

References EMM_Test::getSearchingPaths(), CORE_Integer::parseInt(), CORE_Real::parseReal(), EMM_Test::searchPath(), CORE_String::string2Boolean(), tChar, tIndex, tString, tUIndex, and tUInt.

Referenced by EMM_WaveTest::barWave(), EMM_WaveTest::sharkWave(), EMM_WaveTest::sinusoidalWave(), EMM_WaveTest::trianglePeriodicalWave(), and EMM_WaveTest::triangleWave().

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◆ New()

static SP::EMM_WaveFEMTest EMM_WaveFEMTest::New ( )
inlinestatic

create a test class

References EMM_WaveFEMTest().

Referenced by EMM_DisplacementWaveTest::test().

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◆ null_function()

tReal EMM_WaveTest::null_function ( const tReal t)
staticprotectedinherited

◆ out()

static CORE_Out& CORE_Object::out ( )
inlinestaticinherited

get the output

Returns
the output stream

Referenced by EMM_Matter::adimensionize(), EMM_DisplacementFVMOperator::backup(), EMM_DisplacementOperator::backup(), MATH_ElementaryMultiLevelsToeplitzMatrix::buildSpectralVectorProjector(), EMM_Test::caseTest(), EMM_Test::caseTests(), EMM_MatterField::computeAnisotropyDirectionsField(), EMM_OptimalTimeStep::computeOptimalTimeStep(), MATH_MultiLevelsToeplitzMatrix::copy(), CORE_Exception::CORE_Exception(), EMM_MatterField::createAnisotropyOperator(), CORE_Run::createIO(), EMM_ElementaryTest::defaultBackupTest(), EMM_ElementaryTest::defaultTest(), MATH_MultiLevelsFFTToeplitzMatrix::diagonalize(), EMM_DisplacementFVMOperator::discretize(), EMM_MagnetostrictionOperator::discretize(), EMM_DisplacementFEMOperator::discretize(), EMM_4SymmetricTensors::doubleDot(), EMM_4Tensors::doubleDotCrossDoubleDotScalar(), EMM_TensorsTest::doubleDotCrossDoubleDotScalarTests(), EMM_4Tensors::doubleDotCrossProduct(), EMM_TensorsTest::doubleDotCrossProductTests(), EMM_4Tensors::doubleDotCrossSquaredScalar(), EMM_TensorsTest::doubleDotCrossSquaredScalarTests(), EMM_4Tensors::doubleDotProduct(), EMM_TensorsTest::doubleDotProductTests(), EMM_DisplacementWaveTest::elasticWaveTest(), EMM_Test::elementaryTests(), FFTW_Test::fftwTutorial(), MATH_IntegrationTest::gaussLegendreTest(), EMM_MagnetostrictionTest::HComputingTest(), EMM_DemagnetizedPeriodicalTest::HTest(), EMMH_HysteresisTest::hysteresisDefaultCycleTest(), EMM_TensorsTest::initializationTests(), EMM_MultiScaleGrid::initialize(), EMM_MultiScaleSDGrid::initialize(), EMM_MatterField::loadFromANIFile(), EMM_AnisotropyDirectionsField::loadFromFile(), EMM_Matter::loadFromFile(), EMM_Grid3D::loadFromGEOFile(), EMM_MatterField::loadFromLOCFile(), EMM_Array< tCellFlag >::loadFromStream(), EMM_Matter::loadFromStream(), EMM_Matter::loadMattersFromFile(), EMM_Run::loadSystemFromOptions(), EMM_ElementaryTest::magnetostrictionBackupTest(), CORE_Run::make(), EMMH_Run::makeHysteresis(), EMM_Run::makeRun(), CORE_Run::makeType(), EMM_ElementaryTest::optionsTest(), MATH_PolynomialTest::P4Tests(), EMM_Test::primaryTests(), EMM_LandauLifschitzSystem::printLog(), CORE_Run::printOptions(), EMM_2PackedSymmetricTensors::product(), EMMG_SLDemagnetizedOperator::projectionOnSpectralSpace(), CORE_Run::readOptionsFromCommandLine(), CORE_Test::readVectorTest(), EMM_DemagnetizedPeriodicalTest::relaxationTest(), EMM_DisplacementFVMOperator::restore(), EMM_DisplacementOperator::restore(), EMM_Input::restoreBackup(), EMMH_Hysteresis::run(), EMM_Output::save(), EMM_AnisotropyDirectionsField::saveToFile(), EMM_MatterField::saveToFile(), EMM_Grid3D::saveToGEOFile(), CORE_IOTest::searchTest(), EMMH_Hysteresis::setInitialMagnetizationField(), MATH_MultiLevelsToeplitzMatrix::setLevels(), EMM_4SymmetricTensors::squaredDoubleDot(), EMM_4Tensors::squaredDoubleDotCrossScalar(), EMM_TensorsTest::squaredDoubleDotCrossScalarTests(), EMM_4Tensors::squaredDoubleDotScalar(), EMM_TensorsTest::squaredDoubleDotScalarTests(), EMM_TensorsTest::squaredDoubleDotTests(), EMM_MatterTest::testAdimensionize(), EMM_MatterTest::testANIFile(), CORE_Test::testComplex(), CORE_Test::testDateWeek(), FFTW_Test::testDFT(), EMM_MatterTest::testIO(), EMM_ODETest::testODE(), CORE_Test::testOut(), CORE_Test::testReal(), EMM_FieldTest::testRealArray(), EMM_Grid3DTest::testSegment(), EMM_Grid3DTest::testThinSheet(), CORE_Test::testTime(), CORE_Test::testType(), MATH_FullMatrix::toString(), EMM_DemagnetizedPeriodicalTest::xyPeriodicalCubeSDGTest(), and EMM_DemagnetizedPeriodicalTest::xyPeriodicalSheetSDGTest().

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◆ performanceTest()

tBoolean EMM_Test::performanceTest ( const CORE_Run runner,
const map< tString, tString > &  options 
) const
virtualinherited

make the perfomance tests

Parameters
runnerthe associated runner
optionsthe option sof the test to run
Returns
true if succeeds

Reimplemented from CORE_Test.

Reimplemented in EMM_OperatorsTest.

References CORE_Run::getClassFactory(), tBoolean, and EMM_Test::test().

Referenced by EMM_Test::New().

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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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◆ 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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◆ save() [1/2]

tBoolean EMM_WaveTest::save ( const tString fileName,
const tReal dx,
const tReal U,
const tUIndex nPts 
) const
protectedinherited

save the displacement at time with space space of dx

Parameters
fileNamename of the file to save
dxthe space step
Uthe displacement U
nPts: the number of space step

References tReal, and tUIndex.

Referenced by EMM_WaveFDMTest::waveSystemP1Propagation(), EMM_WaveFDMTest::waveSystemP2Propagation(), EMM_WaveFDMTest::waveTE2Propagation(), and waveTE2Propagation().

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◆ save() [2/2]

tBoolean EMM_WaveTest::save ( const tString fileName,
const tReal dx,
const tReal U,
const tReal V,
const tUIndex nPts 
) const
protectedinherited

save the displacement at time with space space of dx

Parameters
fileNamename of the file to save
dxthe space step
Uthe displacement U
Vthe velocity V
nPts: the number of space step

References tReal, and tUIndex.

◆ searchPath()

tString EMM_Test::searchPath ( const tString fileName) const
inherited

◆ setIsCondensedMassMatrix()

void EMM_WaveFEMTest::setIsCondensedMassMatrix ( const tBoolean isCondensed)
inline

set true if the Mass Matrix is condensed or not

Parameters
isCondensedtrue if the mass matrix is diagonal

References computeCondensedMassMatrix(), computeMassMatrix(), computeStressMatrix(), computeWaveAtFirstTime(), tBoolean, tReal, tString, tUIndex, and waveTE2Propagation().

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◆ 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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◆ 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.

◆ 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
threadthe 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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◆ shark_function()

tReal EMM_WaveTest::shark_function ( const tReal t)
staticprotectedinherited

References EMM_WaveTest::linearPieceWise_function(), tReal, and tUInteger.

Referenced by EMM_WaveTest::sharkWave().

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◆ sharkWave() [1/2]

tBoolean EMM_WaveTest::sharkWave ( const tString method) const
protectedinherited

◆ sharkWave() [2/2]

virtual tBoolean EMM_WaveFEMTest::sharkWave ( ) const
inlineprotectedvirtual

Implements EMM_WaveTest.

References EMM_WaveTest::sharkWave().

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◆ sinusoidal_function()

tReal EMM_WaveTest::sinusoidal_function ( const tReal L,
const tReal U,
const tReal x 
)
staticprotectedinherited

References tReal.

Referenced by EMM_WaveTest::sinusoidalWave().

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◆ sinusoidalWave() [1/2]

tBoolean EMM_WaveTest::sinusoidalWave ( const tString method) const
protectedinherited

◆ sinusoidalWave() [2/2]

virtual tBoolean EMM_WaveFEMTest::sinusoidalWave ( ) const
inlineprotectedvirtual

Implements EMM_WaveTest.

References EMM_WaveTest::sinusoidalWave().

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◆ SP_OBJECT()

EMM_WaveFEMTest::SP_OBJECT ( EMM_WaveFEMTest  )
private

◆ test()

tBoolean EMM_WaveTest::test ( const CORE_Run runner,
const map< tString, tString > &  options 
) const
virtualinherited

make the test

Returns
true if succeeds

Reimplemented from EMM_Test.

References EMM_WaveTest::barWave(), EMM_WaveTest::sharkWave(), EMM_WaveTest::sinusoidalWave(), tBoolean, EMM_WaveTest::trianglePeriodicalWave(), EMM_WaveTest::triangleWave(), and tString.

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◆ testType()

tBoolean CORE_Test::testType ( ) const
inherited

test type

References CORE_Object::getDoubleEpsilon(), CORE_Object::getFloatEpsilon(), CORE_Object::getLDoubleEpsilon(), CORE_Object::getMaxChar(), CORE_Object::getMaxDouble(), CORE_Object::getMaxFlag(), CORE_Object::getMaxFloat(), CORE_Object::getMaxIndex(), CORE_Object::getMaxInt(), CORE_Object::getMaxInteger(), CORE_Object::getMaxLDouble(), CORE_Object::getMaxLInt(), CORE_Object::getMaxLLInt(), CORE_Object::getMaxReal(), CORE_Object::getMaxSInt(), CORE_Object::getMaxUChar(), CORE_Object::getMaxUIndex(), CORE_Object::getMaxUInt(), CORE_Object::getMaxUInteger(), CORE_Object::getMaxULInt(), CORE_Object::getMaxULLInt(), CORE_Object::getMaxUSInt(), CORE_Object::getMinChar(), CORE_Object::getMinDouble(), CORE_Object::getMinFlag(), CORE_Object::getMinFloat(), CORE_Object::getMinIndex(), CORE_Object::getMinInt(), CORE_Object::getMinInteger(), CORE_Object::getMinLDouble(), CORE_Object::getMinLInt(), CORE_Object::getMinLLInt(), CORE_Object::getMinReal(), CORE_Object::getMinSInt(), CORE_Object::getMinUChar(), CORE_Object::getMinUIndex(), CORE_Object::getMinUInt(), CORE_Object::getMinUInteger(), CORE_Object::getMinULInt(), CORE_Object::getMinULLInt(), CORE_Object::getMinUSInt(), CORE_Object::getRealEpsilon(), CORE_Object::getRealInfinity(), CORE_Object::is32Architecture(), CORE_Object::is64Architecture(), CORE_Object::out(), CORE_Out::setVerbose(), tBoolean, tChar, tComplex, tDouble, tFlag, tFloat, tIndex, tInt, tInteger, tLDouble, tLInt, tLLInt, tReal, tSInt, tString, tUChar, tUIndex, tUInt, tUInteger, tULInt, tULLInt, and tUSInt.

Referenced by CORE_Test::New(), and CORE_Test::test().

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◆ toDoAfterThisSetting()

virtual void CORE_Object::toDoAfterThisSetting ( )
inlineprotectedvirtualinherited

method called after setThis() method this method can oly be called once.

Reimplemented in EMM_DisplacementOperator, EMM_DisplacementFVMOperator, EMM_GaussLegendreRelaxation, EMM_GradGaussLegendreRelaxation, and EMM_Object.

Referenced by CORE_Object::setThis().

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◆ toString()

virtual tString CORE_Object::toString ( ) const
inlinevirtualinherited

return the string representation of the object node

Returns
the string representation of the object node

Reimplemented in EMM_DisplacementOperator, EMM_LandauLifschitzSystem, CORE_Array< T >, CORE_Array< tReal >, CORE_Array< tUInteger >, CORE_Array< tString >, CORE_Array< tLimitCondition >, CORE_Array< tUIndex >, CORE_Array< tUChar >, CORE_Array< tCellFlag >, EMM_Grid3D, CORE_Time, CORE_Vector< T >, EMM_Matter, CORE_Out, EMM_DisplacementFEMOperator, EMM_RealField, EMM_DisplacementFVMOperator, CORE_MorseArray< T >, CORE_MorseArray< tReal >, CORE_MorseArray< tUIndex >, CORE_MorseArray< tUChar >, EMM_MagnetostrictionOperator, MATH_MultiLevelsToeplitzMatrix, FFTW_ComplexArray, MATSGN_ComplexArray, EMM_MatterField, CORE_Color, FFTW_Complex, EMM_MultiScaleGrid, MATSGN_Complex, EMM_DisplacementFVM_VTEGROperator, EMM_CondensedMassMatrix, EMM_LandauLifschitzFunction, EMM_Tensors, EMM_DisplacementFVM_SSGROperator, EMMG_SLDemagnetizedOperator, EMM_BlockMassMatrix, CORE_Array2D< T >, EMM_DisplacementFVM_STEGROperator, EMMH_HysteresisFile, EMM_IterativeTimeStep, CORE_SharedPointersVMap< Key, Value >, CORE_SharedPointersVMap< tString, const CORE_Object >, CORE_SharedPointersVMap< tString, CORE_Object >, EMM_AnisotropyDirectionsField, EMM_DemagnetizedOperator, CORE_SharedPointersListVMap< Key, Value >, CORE_String, EMM_OptimalTimeStep, MATH_MaskArrayVector, CORE_SharedPointersKVMap< Key, Value >, MATH_ArrayVector, EMM_Stepper, EMM_CanonicalMassMatrix, MATH_Pn, MATH_FullMatrix, EMMG_SLPeriodicMultiScale, EMM_HyperElasticMatter, MATH_Matrix, CORE_Array3D< T >, EMM_CubicElasticMatter, CORE_Complex, CORE_Integer, CORE_Real, and EMM_MagnetostrictiveMatter.

References CORE_Object::getIdentityString().

Referenced by CORE_Out::genericPrint(), EMM_VelocitySolverTest::massMatrixTrivialSolverTest(), MATH_ConjugateGradient::solve(), CORE_SharedPointersKVMap< Key, Value >::toString(), CORE_SharedPointersListVMap< Key, Value >::toString(), CORE_SharedPointersVMap< tString, CORE_Object >::toString(), EMM_MagnetostrictionOperator::toString(), EMM_Matter::toString(), and EMM_DisplacementOperator::toString().

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◆ triangle_function()

tReal EMM_WaveTest::triangle_function ( const tReal L,
const tReal U,
const tReal x 
)
staticprotectedinherited

References EMM_WaveTest::linearPieceWise_function(), tReal, and tUInteger.

Referenced by EMM_WaveTest::trianglePeriodicalWave(), and EMM_WaveTest::triangleWave().

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◆ trianglePeriodicalWave() [1/2]

tBoolean EMM_WaveTest::trianglePeriodicalWave ( const tString method) const
protectedinherited

◆ trianglePeriodicalWave() [2/2]

virtual tBoolean EMM_WaveFEMTest::trianglePeriodicalWave ( ) const
inlineprotectedvirtual

Implements EMM_WaveTest.

References EMM_WaveTest::trianglePeriodicalWave().

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◆ triangleWave() [1/2]

tBoolean EMM_WaveTest::triangleWave ( const tString method) const
protectedinherited

◆ triangleWave() [2/2]

virtual tBoolean EMM_WaveFEMTest::triangleWave ( ) const
inlineprotectedvirtual

Implements EMM_WaveTest.

References EMM_WaveTest::triangleWave().

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◆ waveSystemP1Propagation()

virtual tBoolean EMM_WaveFEMTest::waveSystemP1Propagation ( const tBoolean isTXTOutput,
const tString prefix,
const tBoolean  dirichletLC[2],
tReal   U_0const tReal &t,
tReal   U_Lconst tReal &t,
const tReal c,
const tReal L,
const tReal dt,
const tUIndex  nT,
EMM_RealArray U,
EMM_RealArray V 
) const
inlineprotectedvirtual

compute the wave at any time from initial conditions U(0,.) and V(0,x) and from dirichlet limit conditions $ U(t,0)=U_0(t) $ or/and $ U(t,L)=U_L(t) $ and/or Neumann limit conditions $ \frac{\partial U}{\partial x}(0) =0 $ or/and $ \frac{\partial U}{\partial x}(L) =0 $ based on solving a system (U,V) :

  • $ \displaystyle V=\frac{\partial U}{\partial t} $
  • $ \displaystyle \frac{\partial V }{\partial t}=c^2. \frac{\partial^2 U}{\partial x^2} $.

This relations imply : $ \displaystyle \frac{\partial^2 V }{\partial t^2}=c^2. \frac{\partial^2 V}{\partial x^2} $

Parameters
isTXTOutput: true to save evolution in TXT files
prefixprefix for saving file
dirichletLClimit condition of dirichlet
U_0: function depending on time t at x=0 if dirichlet condition
U_L: function depending on time t at x=L if dirichlet condition
cthe celerity
Lthe length of the bar
dttime step
nT: the number of time steps
U: initial value of U on x a t=0, returned U(x,t)
V: initial value of velocity at t=0 for all x in [0,L[, returned V(x,t)

Not yet implemented

Implements EMM_WaveTest.

◆ waveSystemP2Propagation()

virtual tBoolean EMM_WaveFEMTest::waveSystemP2Propagation ( const tBoolean isTXTOutput,
const tString prefix,
const tBoolean  dirichletLC[2],
tReal   U_0const tReal &t,
tReal   U_Lconst tReal &t,
const tReal c,
const tReal L,
const tReal cfl,
const tUIndex  nT,
EMM_RealArray U,
EMM_RealArray V 
) const
inlineprotectedvirtual

compute the wave at any time from initial conditions U(0,.) and V(0,x) and from dirichlet limit conditions $ U(t,0)=U_0(t) $ or/and $ U(t,L)=U_L(t)$ and/or Neumann limit conditions $ \frac{\partial U}{\partial x}(0) =0 $ or/and $ \frac{\partial U}{\partial x}(L) =0 $ based on solving a system (V,W)

  • $ \displaystyle V=\frac{\partial U }{\partial t} $
  • $ \displaystyle W=\frac{\partial U }{\partial x} $
  • $ \displaystyle \frac{\partial V }{\partial t}=c^2. \frac{\partial W}{\partial x} $
  • $ \displaystyle \frac{\partial W }{\partial t}= \frac{\partial V }{\partial x} $
Parameters
isTXTOutput: true to save evolution in TXT files
prefixprefix for saving file
dirichletLClimit condition of dirichlet
U_0: function depending on time t at x=0 if dirichlet condition
U_L: function depending on time t at x=L if dirichlet condition
cthe celerity
Lthe length of the bar
cflcondition for convergence cfl=C*dt/dx<=1
nT: the number of time steps
U: initial value of U on x a t=0, returned U(x,t)
V: initial value of velocity at t=0 for all x in [0,L[, returned V(x,t)

Not yet implemented

Implements EMM_WaveTest.

◆ waveTE2Propagation()

tBoolean EMM_WaveFEMTest::waveTE2Propagation ( const tBoolean isForward,
const tBoolean isTXTOutput,
const tString prefix,
const tBoolean isPeriodic,
const tBoolean  dirichletLC[2],
tReal   U_0const tReal &t,
tReal   U_Lconst tReal &t,
const tReal C,
const tReal L,
const tReal cfl,
const tUIndex  nT,
EMM_RealArray U,
EMM_RealArray V 
) const
protectedvirtual

compute the wave at any time from initial conditions U(0,.) and V(0,x) and from dirichlet limit conditions $ U_0(t) $ or/and $ U_L(t) $ and/or Neumann limit conditions $ \frac{\partial U}{\partial x}(0) =0 $ or/and $ \frac{\partial U}{\partial x}(L) =0 $ based on Taylor expansion of order 2 for time: $ \displaystyle \frac{\partial^2 U}{\partial t^2} = c^2. \frac{\partial^2 U}{\partial x^2} $

Parameters
isForward: the first displacement is computing at dt if true. Otherwise, the displacement at -dt is built
isTXTOutput: true to save evolution in TXT files
prefixprefix for saving file
isPeriodicto set if the wave is supposed to be periodic
dirichletLClimit condition of dirichlet
U_0: function depending on time t at x=0 if dirichlet condition
U_L: function depending on time t at x=L if dirichlet condition
Cthe celerity
Lthe length of the bar
cflcondition for convergence cfl=C*dt/dx<=1
nT: the number of time steps
U: initial value of U on x a t=0, returned U(x,t)
V: initial value of velocity at t=0 for all x in [0,L[, returned V(x,t)
  1. compute the displacement U(dt,.) from U(t,.) and U(t-dt,.) with the following formula (see EMM_WaveFEMTest::computeWaveAtFirstTime() ) :

    $ \displaystyle U(dt,.)= \displaystyle U(0,.) + dt. V(0,.) - \frac{c^2.dt^2}{2.dx^2} M^{-1}. X. U(0,.) $

  2. apply the limit conditions to U(dt)
  3. use the following formula, $ \forall t > dt $,

    $ W(.) = \displaystyle - \frac{c^2.dt^2}{dx^2} X. U(t,.) $ where X is defined in EMM_WaveFEMTest::computeStressMatrix() .

For the Dirichlet points i , force $ W(x_i)=U(t,x_i)+U(t-dt,x_i)-2.U(t,x_i) $ when the limit condition at i $ U_i(t), \forall t \geq 0 $ is given.

then $ U(t+dt,.)= M^{-1}. W(.) - U(t-dt,.) + 2.U(t,.) $ where M is defined in EMM_WaveFEMTest::computeMassMatrix() or EMM_WaveFEMTest::computeCondendedMassMatrix() for the condensed mass diagonal matrix.

The stability of the solution is given by finding a solution of the form $ U(t^n,x_k)=\rho^n. e^{i.\omega.k.h}$ where $ h=dx=x_{k+1}-x_k$ within the preceeding formula. It gives:

$ M. D^2_t U(.,.) = -\frac{c^2.dt^2}{dx^2} X. U(t^n,.) $

If M is not condensed:

$ \displaystyle \left ( \rho^{n+1} +\rho^{n-1} -2.\rho^n \right ).\left (\frac{1}{6} . 2 . cos(\omega.h) +\frac{2}{3} \right ) = \displaystyle -s^2. \rho^n \left ( 2-2cos(\omega.x) \right ) $ with $ s=\displaystyle \frac{c.dt}{dx}$.

It leads to $ \rho^2+1-2.\rho +6 \rho . s^2. \displaystyle \frac{1-cos(\omega.h)}{2+cos(\omega.h) } = 0 $

So, $ \rho^2 -2\rho.\alpha +1 = 0 $ with $ \alpha = \displaystyle 1-3.s^2.\frac{1-cos(\omega.h)}{2+cos(\omega.h)} $.

We habe the discriminant $ \Delta= \alpha^2-1 $. If the discriminant is positive then $ \rho > 1 $.

So to be negative, we have to impose that $ |\alpha|\leq 1 $.

It leads to $ s \leq \displaystyle \sqrt{ \frac{2}{3}.\frac{2+cos(\omega.h)}{1-cos(\omega.h)} } $.

As the minimum of the $ f(x)=\displaystyle \frac{2+x}{1-x} $ is 2 on x in [-1,1], if $ s<\frac{1}{\sqrt{3}} $, we have $ |\rho|=1$ which means that the solution is stable.

If M is condensed, we have:

$ \displaystyle \left ( \rho^{n+1} +\rho^{n-1} -2.\rho^n \right ). 1 = \displaystyle -s^2. \rho^n \left ( 2-2cos(\omega.x) \right ) $ with $ s=\displaystyle \frac{c.dt}{dx}$.

So we have $ \displaystyle \rho^2-2.\rho \alpha +1 = 0 $ with $ \alpha=\displaystyle 1-2.s^2.\left(1-cos(\omega dx)\right ) $.

For the same reason as the not condensed matrix case, if we have $ \alpha \geq -1 $, we have $ |\rho|=1 $.

It leads to $ s\leq 1 $ for having a stable solution.

Implements EMM_WaveTest.

References computeCondensedMassMatrix(), EMM_WaveTest::computeEnergy(), computeMassMatrix(), computeStressMatrix(), computeWaveAtFirstTime(), CORE_Array< T >::getSize(), mIsMassMatrixCondensed, MATH_ArrayVector::New(), MATH_FullMatrix::New(), MATH_ConjugateGradient::New(), EMM_WaveTest::save(), CORE_Real::toString(), CORE_Integer::toString(), tReal, tString, and tUIndex.

Referenced by setIsCondensedMassMatrix().

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Member Data Documentation

◆ ALL_TESTS

const tFlag EMM_Test::ALL_TESTS =3
staticinherited

Referenced by EMM_Test::test().

◆ CASE_TEST

const tFlag EMM_Test::CASE_TEST =4
staticinherited

Referenced by EMM_Test::test().

◆ CASE_TESTS

const tFlag EMM_Test::CASE_TESTS =2
staticinherited

Referenced by EMM_Test::test().

◆ ELEMENTARY_TESTS

const tFlag EMM_Test::ELEMENTARY_TESTS =1
staticinherited

Referenced by EMM_Test::test().

◆ mIsMassMatrixCondensed

tBoolean EMM_WaveFEMTest::mIsMassMatrixCondensed
private

◆ PRIMARY_TESTS

const tFlag EMM_Test::PRIMARY_TESTS =0
staticinherited

Referenced by EMM_Test::test().


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