this class is a test class for testing wave equation using the Finite Differences Method: $\displaystyle \frac{\partial^2 u}{\partial t^2} = c^2 . \frac{\partial^2 u}{\partial x^2}$ More...

#include <EMM_WaveFDMTest.h>

Inheritance diagram for EMM_WaveFDMTest:

[legend]

Collaboration diagram for EMM_WaveFDMTest:

[legend]

Public Member Functions
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_WaveFDMTest	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_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	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
tBoolean	computeWaveAtPreviousTime (const tBoolean &isPeriodic, const tBoolean dirichletLC[2], tReal U0(const tReal &t), tReal UL(const tReal &t), const EMM_RealArray &Ux_0, const EMM_RealArray &dU_dt0, const tReal &s2, const tReal &dt, EMM_RealArray &Ux_1) const
	compute the wave U(-dt,.) with Dirichlet/Neumann limit conditions. More...

tBoolean	computeWaveAtFirstTime (const tBoolean &isPeriodic, const tBoolean dirichletLC[2], tReal U0(const tReal &t), tReal UL(const tReal &t), const EMM_RealArray &Ux_0, const 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	computeVelocityWaveAtPreviousTime (const tBoolean &isPeriodic, const tBoolean dirichletLC[2], tReal U0(const tReal &t), tReal UL(const tReal &t), const EMM_RealArray &Ux_0, const EMM_RealArray &Vx_0, const tReal &c, const tReal &dt, const tReal &dx, EMM_RealArray &dU_dt) const
	compute the velocity wave V(-dt,.) with Dirichlet/Neumann limit conditions. 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 or/and 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 dirichletCL[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 or/and 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 or/and 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_WaveFDMTest)

	EMM_WaveFDMTest (void)
	create the class More...

virtual	~EMM_WaveFDMTest (void)
	destroy the class More...

Detailed Description

this class is a test class for testing wave equation using the Finite Differences Method: $\displaystyle \frac{\partial^2 u}{\partial t^2} = c^2 . \frac{\partial^2 u}{\partial x^2}$

The aproximation of time is either

Taylor Expansion of order 2 : $\displaystyle \frac{\partial^2 f}{\partial t^2 } = \displaystyle \frac{f(t+dt)+f(t-dt)-2.f(t)}{dt^2}$ and $\frac{\partial^2 f}{\partial x^2 } = \displaystyle \frac{f(x+dx)+f(x-dx)-2.f(x)}{dt^2}$ (see EMM_WaveFDMTest::waveTE2Propagation() )
a system or order 1 with 2 variables : displacement and velocity (see EMM_WaveFDMTest::waveSystemP1Propagation() ).
- $\displaystyle V=\frac{\partial U}{\partial t}$
- $\displaystyle \frac{\partial V }{\partial t}=c^2. \frac{\partial^2 U}{\partial x^2}$
a system of order 1 with 2 varaibles : velocity and deformation (see EMM_WaveFDMTest::waveSystemP2Propagation() ).
- $\displaystyle V=\frac{\partial U }{\partial t}$
- $\displaystyle W=\frac{\partial U }{\partial x}$
- $\displaystyle \frac{\partial V }{\partial t}=c^2. \frac{\partial W}{\partial x}$
- $\displaystyle \frac{\partial W }{\partial t}= \frac{\partial V }{\partial x}$
Author
Stéphane Despréaux

Version
1.0

Constructor & Destructor Documentation

◆ EMM_WaveFDMTest()

EMM_WaveFDMTest::EMM_WaveFDMTest ( void )

private

create the class

Referenced by New().

Here is the caller graph for this function:

◆ ~EMM_WaveFDMTest()

EMM_WaveFDMTest::~EMM_WaveFDMTest ( void )

privatevirtual

destroy the class

Member Function Documentation

◆ barWave() [1/2]

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

protectedinherited

References EMM_Test::caseTest(), CORE_Array< T >::initArray(), EMM_WaveTest::linearPieceWise_function(), EMM_WaveTest::load(), EMM_WaveTest::null_function(), CORE_Array< T >::setSize(), tBoolean, tReal, tString, tUIndex, tUInteger, tUSInt, EMM_WaveTest::waveSystemP1Propagation(), EMM_WaveTest::waveSystemP2Propagation(), and EMM_WaveTest::waveTE2Propagation().

Here is the call graph for this function:

◆ barWave() [2/2]

virtual tBoolean EMM_WaveFDMTest::barWave ( ) const

inlineprotectedvirtual

Implements EMM_WaveTest.

References EMM_WaveTest::barWave().

Here is the call graph for this function:

◆ compareField()

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

staticinherited

compare 2 fields

Parameters

F	the field to compare
G	the secund field to compare
indexMax	the 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().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ 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
C	celerity of the wave
dx	space step size
dt	time step size
U	: U at t
Ut	U at t+dt

References null, tReal, and tUIndex.

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

Here is the caller graph for this function:

◆ 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}

◆ 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().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ 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().

Here is the call graph for this function:

◆ computeVelocityWaveAtPreviousTime()

tBoolean EMM_WaveFDMTest::computeVelocityWaveAtPreviousTime	(	const tBoolean &	isPeriodic,
		const tBoolean	dirichletLC[2],
		tReal	U0const tReal &t,
		tReal	ULconst tReal &t,
		const EMM_RealArray &	Ux_0,
		const EMM_RealArray &	Vx_0,
		const tReal &	c,
		const tReal &	dt,
		const tReal &	dx,
		EMM_RealArray &	dU_dt
	)		const

protected

compute the velocity wave V(-dt,.) with Dirichlet/Neumann limit conditions.

Parameters

isPeriodic	the wave is supposed to be periodic
dirichletLC	limit 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]
Vx_0	: initial value of V at t=0 for all x in [0,L]
c	celerity of the wave
dt	time step
dx	space step
dU_dt	: return the values of V at t-dt

V(t-dt,x)=V(t,x)-dt.(dV/dt)(t,x)+dt^2*c^2*d2V/(2*dx^2)

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

$\displaystyle \frac{\partial V}{\partial t}(t,x)= c^2 \displaystyle \frac{\partial^2 U}{\partial x^2}(t,x)$

$\displaystyle \frac{\partial^2 V}{\partial t^2}(t,x)= c^2 \displaystyle \frac{\partial^2 V}{\partial x^2}(t,x)$

$\Rightarrow \displaystyle V(t+dt,x)= V(t,x)-\displaystyle dt.c^2 \frac{U(0,x+dx)+U(0,x-dx)-2.U(0,x) }{dx^2} + \frac{dt^2.c^2}{2} \frac{V(0,x+dx)+V(0,x-dx)-2.V(0,x) }{dx^2}$

At boundary x=0
- if Dirichlet limit condition, then
- if Neumann limit conidtion, then $V(-dt,0)=V(t,0)-dt*c^2*\frac{U(0,2.dx)+U(0,0)-2.U(0,dx) }{dx^2} + \frac{dt^2.c^2}{2} \frac{V(0,2.dx)+V(0,0)-2.V(0,dx) }{dx^2}$
At boundary x=L
- if Dirichlet limit condition, then
- if Neumann, limit conditionn, then $V(-dt,0)=V(t,L)-dt*c^2*\frac{U(0,L-2.dx)+U(0,L)-2.U(0,L-dx) }{dx^2} + \frac{dt^2.c^2}{2} \frac{V(0,L-2.dx)+V(0,L)-2.V(0,L-dx) }{dx^2}$

References CORE_Array< T >::getSize(), tReal, and tUIndex.

Referenced by New(), and waveSystemP1Propagation().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ computeWaveAtFirstTime()

tBoolean EMM_WaveFDMTest::computeWaveAtFirstTime	(	const tBoolean &	isPeriodic,
		const tBoolean	dirichletLC[2],
		tReal	U0const tReal &t,
		tReal	ULconst tReal &t,
		const EMM_RealArray &	Ux_0,
		const EMM_RealArray &	dU_dt0,
		const tReal &	s,
		const tReal &	dt,
		EMM_RealArray &	Ux_1
	)		const

protected

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

Parameters

isPeriodic	the wave is supposed to be periodic
dirichletLC	limit 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[
s	the quantity $\frac{c^2*dt^2}{dx^2}$
dt	: the time step
Ux_1	: return the values of U at t=dt

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

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

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

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

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

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

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

so we deduce at first step that : $\displaystyle U(t+dt,x)= \displaystyle \left (1-c^2 \frac{dt^2}{dx^2} \right ).U(t,x)+c^2 \frac{dt^2}{2.dx^2} \left ( U(t,x+dx)+U(t,x-dx) \right ) + dt*\frac{\partial U}{\partial t}(0,x)$

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

if the boundary limit condition on x=0 is Dirichlet , we have $ U(dt,0)=U_0(dt) $ if the boundary limit condition on x=0 is Neumann , to maintain a 2-order in dx, we have $U(dt,0)=\frac{4*U(dt,dx)-U(dt,2dx)}{3}$ if the boundary limit condition on x=L is Dirichlet , we have $ U(dt,L)=U_L(dt) $ if the boundary limit condition on x=L is Neumann , to maintain a 2-order in dx, we have $U(dt,L)=\frac{4*U(dt,L-dx)-U(dt,L-2dx)}{3}$

References CORE_Array< T >::getSize(), CORE_Array< T >::setSize(), tReal, and tUIndex.

Referenced by New(), and waveTE2Propagation().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ computeWaveAtPreviousTime()

tBoolean EMM_WaveFDMTest::computeWaveAtPreviousTime	(	const tBoolean &	isPeriodic,
		const tBoolean	dirichletLC[2],
		tReal	U0const tReal &t,
		tReal	ULconst tReal &t,
		const EMM_RealArray &	Ux_0,
		const EMM_RealArray &	dU_dt0,
		const tReal &	s2,
		const tReal &	dt,
		EMM_RealArray &	Ux_1
	)		const

protected

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

Parameters

isPeriodic	the wave is supposed to be periodic
dirichletLC	limit condition of dirichlet 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

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[
s2	the quantity $\frac{c^2*dt^2}{dx^2}$
dt	: the time step
Ux_1	: return the values of U at t=-dt

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

But, $\displaystyle \frac{\partial^2 U}{\partial t^2} (t,x)= c^2 \displaystyle \frac{\partial^2 U}{\partial x^2}(t,x)$

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

if the boundary limit condition on x=0 is Dirichlet , we have $ U(-dt,0)=U_0(-dt) $ if the boundary limit condition on x=0 is Neumann , to maintain a 2-order in dx, we have $U(-dt,0)=\frac{4*U(-dt,dx)-U(-dt,2dx)}{3}$ if the boundary limit condition on x=L is Dirichlet , we have $ U(-dt,L)=U_L(-dt) $ if the boundary limit condition on x=L is Neumann , to maintain a 2-order in dx, we have $U(-dt,L)=\frac{4*U(-dt,L-dx)-U(-dt,L-2dx)}{3}$

References CORE_Array< T >::getSize(), CORE_Array< T >::setSize(), tReal, and tUIndex.

Referenced by New(), waveSystemP1Propagation(), and waveTE2Propagation().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ createBox()

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

staticinherited

create a box

Parameters

dim	dimension of a parallelipiped box in each direction
N	number 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().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ createCube()

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

staticinherited

create a cube

Parameters

dim	dimension of a parallelipiped cube in each direction
N	number 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().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ 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().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ 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().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ 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().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the call graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ getSearchingPaths()

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

inherited

get the path fro seaching the files

Parameters

vpaths the vectors of searching paths

References tString, and tUSInt.

Referenced by EMM_ElementaryTest::defaultBackupTest(), EMM_ElementaryTest::defaultTest(), EMM_DemagnetizedTest::demagnetizedTestCase(), EMM_DisplacementWaveTest::elasticWaveTest(), EMM_DemagnetizedPeriodicalTest::HTest(), EMMH_HysteresisTest::hysteresisDefaultCycleTest(), EMM_WaveTest::load(), EMM_ElementaryTest::magnetostrictionBackupTest(), EMM_Test::New(), EMM_DemagnetizedPeriodicalTest::periodicalDemagnetizedTestCase(), EMM_DemagnetizedPeriodicalTest::relaxationTest(), EMM_Test::searchPath(), EMM_CaseTest::testCase(), EMM_ODETest::testODE(), EMM_FieldTest::testRealArray(), EMM_DemagnetizedPeriodicalTest::xyPeriodicalCubeSDGTest(), and EMM_DemagnetizedPeriodicalTest::xyPeriodicalSheetSDGTest().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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

Here is the caller graph for this function:

◆ 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().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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

dim	dimension of the parallelepiped cube
x	coordinates 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().

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the call graph for this function:

◆ 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().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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

optionFile	name of the file containing lines key=value The keys are "dirichlet0" "dirichlet1" "L" "nPoints" "Umax" "C" "nTimes" "cfl" "txt-output"
path	the 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
L	the length of the 1D-domain
nPoints	: number of discretized points on x
Umax	the maximum amplitude of U
C	the celerity of the wave
nTimes	the number of time steps
cfl	the 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().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ New()

static SP::EMM_WaveFDMTest EMM_WaveFDMTest::New ( )

inlinestatic

create a test class

References computeVelocityWaveAtPreviousTime(), computeWaveAtFirstTime(), computeWaveAtPreviousTime(), EMM_WaveFDMTest(), tBoolean, tReal, tString, tUIndex, waveSystemP1Propagation(), waveSystemP2Propagation(), and waveTE2Propagation().

Referenced by EMM_DisplacementWaveTest::test().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ null_function()

tReal EMM_WaveTest::null_function ( const tReal & t )

staticprotectedinherited

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

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ performanceTest()

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

virtualinherited

make the perfomance tests

Parameters

runner	the associated runner
options	the 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().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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.

Here is the call graph for this function:

◆ printObjectsInMemory() [2/2]

static void CORE_Object::printObjectsInMemory ( )

inlinestaticinherited

print object in memory in the standart output

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

Here is the caller graph for this function:

◆ resetOut()

static void CORE_Object::resetOut ( )

inlinestaticinherited

reset the output stream

Referenced by run().

Here is the caller graph for this function:

◆ resetThread()

static void CORE_Object::resetThread ( )

inlinestaticinherited

reset the output stream

Referenced by run().

Here is the caller graph for this function:

◆ 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

fileName	name of the file to save
dx	the space step
U	the displacement U
nPts	: the number of space step

References tReal, and tUIndex.

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

Here is the caller graph for this function:

◆ 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

fileName	name of the file to save
dx	the space step
U	the displacement U
V	the velocity V
nPts	: the number of space step

References tReal, and tUIndex.

◆ searchPath()

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

inherited

set the path to find the file with name fileName

Parameters

fileName name of the file

Returns: the path to find the file. Return empty path if not found

References CORE_IO::exists(), and EMM_Test::getSearchingPaths().

Referenced by EMM_Test::computeMField(), EMM_ElementaryTest::defaultBackupTest(), EMM_ElementaryTest::defaultTest(), EMM_DemagnetizedTest::demagnetizedTestCase(), EMM_DisplacementWaveTest::elasticWaveTest(), EMM_DemagnetizedPeriodicalTest::HTest(), EMMH_HysteresisTest::hysteresisCycleTest(), EMMH_HysteresisTest::hysteresisDefaultCycleTest(), EMM_WaveTest::load(), EMM_ElementaryTest::magnetostrictionBackupTest(), EMM_Test::New(), EMM_DemagnetizedPeriodicalTest::periodicalDemagnetizedTestCase(), EMM_DemagnetizedPeriodicalTest::relaxationTest(), EMM_MatterTest::testAdimensionize(), EMM_MatterTest::testANIFile(), EMM_CaseTest::testCase(), EMM_MatterTest::testIO(), EMM_ODETest::testODE(), EMM_FieldTest::testRealArray(), EMM_Grid3DTest::testSegment(), EMM_Grid3DTest::testThinSheet(), EMM_DemagnetizedPeriodicalTest::xyPeriodicalCubeSDGTest(), and EMM_DemagnetizedPeriodicalTest::xyPeriodicalSheetSDGTest().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the call graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ shark_function()

tReal EMM_WaveTest::shark_function ( const tReal & t )

staticprotectedinherited

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

Referenced by EMM_WaveTest::sharkWave().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ sharkWave() [1/2]

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

protectedinherited

References EMM_Test::caseTest(), CORE_Array< T >::initArray(), EMM_WaveTest::load(), EMM_WaveTest::null_function(), CORE_Array< T >::setSize(), EMM_WaveTest::shark_function(), tBoolean, tReal, tString, tUIndex, tUSInt, EMM_WaveTest::waveSystemP1Propagation(), EMM_WaveTest::waveSystemP2Propagation(), and EMM_WaveTest::waveTE2Propagation().

Here is the call graph for this function:

◆ sharkWave() [2/2]

virtual tBoolean EMM_WaveFDMTest::sharkWave ( ) const

inlineprotectedvirtual

Implements EMM_WaveTest.

References EMM_WaveTest::sharkWave().

Here is the call graph for this function:

◆ sinusoidal_function()

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

staticprotectedinherited

References tReal.

Referenced by EMM_WaveTest::sinusoidalWave().

Here is the caller graph for this function:

◆ sinusoidalWave() [1/2]

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

protectedinherited

References EMM_Test::caseTest(), CORE_Array< T >::initArray(), EMM_WaveTest::load(), EMM_WaveTest::null_function(), CORE_Array< T >::setSize(), EMM_WaveTest::sinusoidal_function(), tBoolean, tReal, tString, tUIndex, tUSInt, EMM_WaveTest::waveSystemP1Propagation(), EMM_WaveTest::waveSystemP2Propagation(), and EMM_WaveTest::waveTE2Propagation().

Here is the call graph for this function:

◆ sinusoidalWave() [2/2]

virtual tBoolean EMM_WaveFDMTest::sinusoidalWave ( ) const

inlineprotectedvirtual

Implements EMM_WaveTest.

References EMM_WaveTest::sinusoidalWave().

Here is the call graph for this function:

◆ SP_OBJECT()

EMM_WaveFDMTest::SP_OBJECT ( EMM_WaveFDMTest )

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.

Here is the call graph for this function:

◆ testType()

tBoolean CORE_Test::testType ( ) const

inherited

test type

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

Here is the call graph for this function:

Here is the caller graph for this function:

◆ 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().

Here is the caller graph for this function:

◆ 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().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ 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().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ trianglePeriodicalWave() [1/2]

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

protectedinherited

References EMM_Test::caseTest(), CORE_Array< T >::initArray(), EMM_WaveTest::load(), EMM_WaveTest::null_function(), CORE_Array< T >::setSize(), tBoolean, tReal, EMM_WaveTest::triangle_function(), tString, tUIndex, tUSInt, EMM_WaveTest::waveSystemP1Propagation(), EMM_WaveTest::waveSystemP2Propagation(), and EMM_WaveTest::waveTE2Propagation().

Here is the call graph for this function:

◆ trianglePeriodicalWave() [2/2]

virtual tBoolean EMM_WaveFDMTest::trianglePeriodicalWave ( ) const

inlineprotectedvirtual

Implements EMM_WaveTest.

References EMM_WaveTest::trianglePeriodicalWave().

Here is the call graph for this function:

◆ triangleWave() [1/2]

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

protectedinherited

References EMM_Test::caseTest(), CORE_Array< T >::initArray(), EMM_WaveTest::load(), EMM_WaveTest::null_function(), CORE_Array< T >::setSize(), tBoolean, tReal, EMM_WaveTest::triangle_function(), tString, tUIndex, tUSInt, EMM_WaveTest::waveSystemP1Propagation(), EMM_WaveTest::waveSystemP2Propagation(), and EMM_WaveTest::waveTE2Propagation().

Here is the call graph for this function:

◆ triangleWave() [2/2]

virtual tBoolean EMM_WaveFDMTest::triangleWave ( ) const

inlineprotectedvirtual

Implements EMM_WaveTest.

References EMM_WaveTest::triangleWave().

Here is the call graph for this function:

◆ waveSystemP1Propagation()

tBoolean EMM_WaveFDMTest::waveSystemP1Propagation	(	const tBoolean &	isTXTOutput,
		const tString &	prefix,
		const tBoolean	dirichletCL[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

protectedvirtual

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
prefix	prefix for saving file
dirichletCL	limit 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
c	the celerity
L	the length of the bar
dt	time 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)

compute the displacement U(-dt,x) at order 2 in time from U(0,x) and from the velocity dU_dt(0,x) for all x in [0,L[ with the formula :

$U(-dt,x)=U(0,x)-dt.V(0,x) + \displaystyle \frac{dt^2.c^2}{2}. \frac{\partial^2 U}{\partial x^2}(0,x)$
compute the velocity at order 2 in time : V(-dt,x) from U(0,x) and the velocity dU_dt(0,x) for all x in [0,L[ with the formula :

$V(-dt,x)=V(0,x)-dt.c^2. \frac{\partial^2 U}{\partial x^2}(0,x) - \frac{dt^2.c^2}{2} \frac{\partial^2 V}{\partial x^2}(0,x)$
at any time t > 0
- compute the secund space variation of U : $\partial^2 U=U(t,x+dx)+U(t,x-dx,t)-2.U(t,x)$
- compute the secund space variation of V : $\partial^2 V=V(t,x+dx)+V(t,x-dx,t)-2.V(t,x)$
- compute the displacement U with the formula $\displaystyle U(t+dt,x)=U(t,x)+dt.V(t,x)+\frac{dt^2.c^2}{2} \frac{ \partial^2 U}{\partial x^2 }$
- compute the displacement V with the formula $\displaystyle V(t+dt,x)=V(t,x)+dt.c^2. \frac{\partial^2 U}{\partial x^2}$
use the dirichlet limit condition for all t at x=0 and x=L: for example,
- if dirichlet condition on x=0 :
  - $V(t+dt,0)=\displaystyle \frac{U_0(t+dt)-U_0(t)}{dt}$
- if neumann condition on x=0 :
  - $V(t+dt,0)=\displaystyle \frac{U(t+dt,0)-U(t,0)}{dt}= \displaystyle \frac{U(t+dt,dx)-U(t,0)}{dt}$

For studying the stability of the solution, we suppose $U(t^n,x_k)=P^n. e^{i.\omega.k.h}$ and $V(t^n,x_k)=Q^n. e^{i.\Omega.k.h}$ where $h=dx=x_{k+1}-x_k$ . It gives:

$P^{n+1}=P^n+dt.Q^n.e^{i\theta_k} - \displaystyle \frac{dt^2.c^2}{h^2}.P^n.(1-cos(\omega.h))$ where $\theta_k=(\Omega-\omega).k.h$
$Q^{n+1}=Q^n - \displaystyle 2.\frac{dt.c^2}{h^2}.P^n.e^{-i\theta_k}(1-cos(\omega.h))$

with $s=\frac{c.dt}{h}$ and $\lambda=s^2.(1-cos(\omega.h))$ ,

$P^{n+1}=\displaystyle P^n+dt.Q^n.e^{i\theta_k} - \lambda.P^n$
$Q^{n+1}=\displaystyle Q^n - 2.\frac{\lambda}{dt}.P^n.e^{-i\theta_k}$

So with,

$P^n= \displaystyle - \frac{dt.e^{i\theta_k}}{2.\lambda} \left ( Q^{n+1}-Q^{n} \right )$ ,

we obtain

$\displaystyle \left ( Q^{n+2}-Q^{n+1} \right ) = \displaystyle \left ( Q^{n+1}-Q^{n} \right ) - 2.\lambda Q^n. - \lambda. \left ( Q^{n+1}-Q^{n} \right )$

so, $\displaystyle Q^{2}-Q = Q-1 - 2.\lambda - \lambda. \left ( Q-1 \right )$

We have to find Q such that $|Q| \leq 1$ and $Q^2+ (\lambda-2).Q + (1 + \lambda) = 0$ .

The discriment is $\Delta=\lambda.(\lambda-8)$ .

If $\Delta \geq 0$ , then $Q=(\lambda/2.-1) + \sqrt{\Delta}/2 > 1$ , so the solution is unstable.
If $\Delta < 0$ , then $Q= (\lambda/2.-1) \pm i \sqrt{-\Delta}/2$ whose module $|Q|^2= 1+\lambda > 1$ . So the solution is always unstable.

Implements EMM_WaveTest.

References computeVelocityWaveAtPreviousTime(), computeWaveAtPreviousTime(), CORE_Array< T >::getSize(), EMM_WaveTest::save(), CORE_Real::toString(), CORE_Integer::toString(), tReal, tString, and tUIndex.

Referenced by New().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ waveSystemP2Propagation()

tBoolean EMM_WaveFDMTest::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

protectedvirtual

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 generate output files
prefix	prefix for saving file
dirichletLC	limit 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
c	the celerity
L	the length of the bar
cfl	condition 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)

compute $W(0,x)= \frac{\partial U(0,x)}{\partial x}$
for all time :
- compute
- compute
- compute
- compute
- compute $V(t+dt,x)=V(t,x)+dt. c^2 \frac{dW_x}{2.dx} + dt^2.c^2 \frac{d^2V_x}{2.dx^2}$
- compute $W(t+dt,x)=W(t,x)+dt. \frac{dV_x}{2.dx} + dt^2.c^2 \frac{d^2W_x}{2.dx^2}$
- compute optional U $U(t+dt,x)=U(t,x)+dt.V(t,x) + \frac{dt^2.c^2.dW_x}{4.dx} + \frac{dt^3.c^2.d2V_x}{6.dx^2}$
- apply the limit conditions:
  - if dirichlet on x=0
    - $V(t+dt,0)=\frac{\partial U(0,t)}{\partial t}$
    - ( $\frac{\partial W}{\partial x}=0$ )
  - else if neumann on x=0
    - ( $\frac{\partial U}{\partial x}=0$ )
    - $V(t+dt,0)=V(dx,t)+\frac{dt.c^2.dW_x}{4.dx}+\frac{dt^2.c^2.d2V_x}{6.dx^2}$ because $V(t+dt,0)=\frac{\partial U}{\partial t}=\frac{U(t+dt,0)-U(t,0)}{dt}$ and , and $U(t+dt,dx)-U(t,dx)=dt.V(t,dx)+\frac{dt^2.c^2.dW_x}{4.dx} +\frac{dt^3.c^2.d^2V_x}{6.dx^2}$

For studying the stability of the solution, we can transform the system by usig the variable U(t,x)=[V(t,x),W(t,x)], we have the Tyalor expansion at ordeer 2 in time

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

As we have $\displaystyle \frac{\partial U }{\partial t}=A. \frac{\partial U }{\partial x}$ with

$A = \left[ {\begin{array}{cc} 0 & c^2 \\ 1 & 0 \end{array} } \right]$

As A can be diagonilized with two different eigen values c and -c, we can study the stability in each coordinate of the eigen vectors basis:

By denoting by $\tilde U_d$ the d-coordinate of the vector U in the eigen vector basis we have:

$\tilde U_d(t+dt,x)=\displaystyle \tilde U(t,x)+\frac{\epsilon_d c.dt}{2.dx} \left (\tilde U_d(t,x+dx)-\tilde U_d(t,x-dx)\right ) + \frac{c^2. dt^2}{2.dx^2} \left( \tilde U_d(t,x+dx)+ \tilde U_d(t,x-dx)-2.\tilde U_d(t,x) \right )$ .

To study the stability , we find the solution $\tilde U_d(t,x)=\rho^n . e^{i.\omega.k.dx}$ . So, we obtain:

$\rho = \displaystyle 1+ \frac{\epsilon_d.c.dt}{dx} i. sin(\omega dx) -\frac{c^2. dt^2}{dx^2} \left (1-cos(\omega.dx) \right )$ .

So the module of $\rho$ is $|\rho|^2=\displaystyle \left (1-s^2.(1-cos(\omega.dx) \right )^2 + s^2. sin^2(\omega.dx)$ when $s=\displaystyle \frac{c.dt}{dx}$ .

So, $|\rho| \leq 1$ implies $s \leq \displaystyle \frac{2}{1-cos(\omega.dx)} -\frac{sin^2(\omega.dx)}{\left(1-cos(\omega.dx)\right )^2 }=1$ . undex the condion $ d_leq 1 $ with have the satiblity of the solution

Implements EMM_WaveTest.

References EMM_WaveTest::computeEnergy(), CORE_Array< T >::getSize(), EMM_WaveTest::save(), CORE_Real::toString(), CORE_Integer::toString(), tReal, tString, and tUIndex.

Referenced by New().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ waveTE2Propagation()

tBoolean EMM_WaveFDMTest::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
prefix	prefix for saving file
isPeriodic	the wave is supposed to be periodic
dirichletLC	limit 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
C	the celerity
L	the length of the bar
cfl	condition 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(t,x)
V	: initial value of velocity at t=0 for all x in [0,L[, returned V(t,x)

compute the displacement U(dt,x) from U(0,x) and U(-dt,x) for all x in [0,L[ with the following formula (see computeWaveAtFirstTime() ) :

$\displaystyle U(dt,x)= \displaystyle U(0,x) + dt. V(0,x) + \frac{c^2.dt^2}{2.dx^2} \left ( U(0,x+dx)+U(0,x-dx)-2.U(0,x)\right )$

$\Rightarrow \displaystyle U(dt,x)= \displaystyle (1-s^2). U(0,x) + dt. V(0,x) + \frac{s^2}{2}. \left ( U(0,x+dx)+U(0,x-dx) \right )$ with $\displaystyle s=\frac{c.dt}{dx}$
use the following formula: As $\displaystyle \frac{\partial^2 U}{\partial t^2} = \displaystyle \frac{U(t+dt,.)+U(t-dt,.x)-2/U(t,.)}{dt^2}$ , we have

$\forall t >dt, U(t+dt,x) = \displaystyle 2. (1- s^2) U(t,x) + s^2 \displaystyle \left ( U(t,x+dx)+U(t,x-dx) \right ) - U(t-dt,x)$
update the limit conditions :
- if the boundary limit condition on x=0 is Dirichlet , we have
- if the boundary limit condition on x=0 is Neumann , to maintain a 2-order in dx, we have $U(t+dt,0)=\frac{4*U(t+dt,dx)-U(t+dt,2dx)}{3}$
- if the boundary limit condition on x=L is Dirichlet , we have
- if the boundary limit condition on x=L is Neumann , to maintain a 2-order in dx, we have $U(t+dt,L)=\frac{4*U(t+dt,L-dx)-U(t+dt,L-2dx)}{3}$

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:

$\rho^2 +1 -2.\alpha \rho = 0$ with $\alpha= 1-s^2.(1-cos(w.h))$ .

To have a solution with module less than one, we need to have a negative discriminant i.e; $-1 \leq \alpha \leq 1$ which leads to

$\displaystyle s \leq \sqrt{\frac{2}{1-cos(wh)}}$ .

As $\displaystyle \sqrt{\frac{2}{1-cos(wh)}}>=1$ , if we have $ s<=1 $ , then algorithm is stable.

Implements EMM_WaveTest.

References EMM_WaveTest::computeEnergy(), computeWaveAtFirstTime(), computeWaveAtPreviousTime(), CORE_Array< T >::getSize(), EMM_WaveTest::save(), CORE_Real::toString(), CORE_Integer::toString(), tReal, tString, and tUIndex.

Referenced by New().

Here is the call graph for this function:

Here is the caller graph for this function:

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().

◆ 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:

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Static Protected Member Functions

Private Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ EMM_WaveFDMTest()

◆ ~EMM_WaveFDMTest()

Member Function Documentation

◆ barWave() [1/2]

◆ barWave() [2/2]

◆ compareField()

◆ computeEnergy()

◆ computeEpsilon()

◆ computeMField() [1/2]

◆ computeMField() [2/2]

◆ computeVelocityWaveAtPreviousTime()

◆ computeWaveAtFirstTime()

◆ computeWaveAtPreviousTime()

◆ createBox()

◆ createCube()

◆ createDomain()

◆ createMatters()

◆ createSystem()

◆ getClassName() [1/2]

◆ getClassName() [2/2]

◆ getDoubleEpsilon()

◆ getDoubleInfinity()

◆ getEpsilon()

◆ getFloatEpsilon()

◆ getFloatInfinity()

◆ getIdentityString()

◆ getInfinity()

◆ getLDoubleEpsilon()

◆ getLDoubleInfinity()

◆ getMaxChar()

◆ getMaxDouble()

◆ getMaxFlag()

◆ getMaxFloat()

◆ getMaxIndex()

◆ getMaxInt()

◆ getMaxInteger()

◆ getMaxLDouble()

◆ getMaxLInt()

◆ getMaxLLInt()

◆ getMaxReal()

◆ getMaxSInt()

◆ getMaxUChar()

◆ getMaxUIndex()

◆ getMaxUInt()

◆ getMaxUInteger()

◆ getMaxULInt()

◆ getMaxULLInt()

◆ getMaxUSInt()

◆ getMinChar()

◆ getMinDouble()

◆ getMinFlag()

◆ getMinFloat()

◆ getMinIndex()

◆ getMinInt()

◆ getMinInteger()

◆ getMinLDouble()

◆ getMinLInt()

◆ getMinLLInt()

◆ getMinReal()

◆ getMinSInt()

◆ getMinUChar()

◆ getMinUIndex()

◆ getMinUInt()

◆ getMinUInteger()

◆ getMinULInt()

◆ getMinULLInt()

◆ getMinUSInt()

◆ getOut()

◆ getPointerAddress()

◆ getRealEpsilon()

◆ getRealInfinity()

◆ getSearchingPaths()