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Namespaces
namespace	internal

Data Structures
class	CCZ4

class	FiniteVolumeCCZ4

class	RKDGCCZ4

Functions
KeywordToAvoidDuplicateSymbolsForInlinedFunctions void	ncp (double BgradQ, const double const Q, const double *const gradQSerialised, const int normal, const int CCZ4LapseType, const double CCZ4ds, const double CCZ4c, const double CCZ4e, const double CCZ4f, const double CCZ4bs, const double CCZ4sk, const double CCZ4xi, const double CCZ4mu, const double CCZ4SO) InlineMethod

KeywordToAvoidDuplicateSymbolsForInlinedFunctions void	source (double S, const double const Q, const int CCZ4LapseType, const double CCZ4ds, const double CCZ4c, const double CCZ4e, const double CCZ4f, const double CCZ4bs, const double CCZ4sk, const double CCZ4xi, const double CCZ4itau, const double CCZ4eta, const double CCZ4k1, const double CCZ4k2, const double CCZ4k3, const double CCZ4SO) InlineMethod
	The source term is one out of two terms that we use in our CCZ4 formulation.

KeywordToAvoidDuplicateSymbolsForInlinedFunctions double	maxEigenvalue (const double *const Q, int normal, const double CCZ4e, const double CCZ4ds, const double CCZ4GLMc, const double CCZ4GLMd) InlineMethod

void	admconstraints (double constraints, const double const Q, const double *const gradQSerialised)
	This is a postprocessing routine to monitor if the physical constraints are fulfilled.

void	ThetaOutputNCP (double NCPterm, const double const Q, const double *const gradQSerialised, int normal)
	A temporary test function, to output Hamilton constraint related term in theta, 1 terms: RPlusTwoNablaZNCP.

void	TestingOutput (double terms, const double const Q, const double *const gradQSerialised)
	A temporary test function, to output some testing values 0,1 entries: Hamilton constraint related term in theta, 2 terms: RPlusTwoNablaZSrc, pure Src 2-10 entry: no-symmetry version of R_ij.

void	Psi4Calc (double Psi4, const double const Q, const double const gradQSerialised, double coor)
	This function is for the calculation of psi4, a quantity related to gravitional wave.

void	enforceCCZ4constraints (double *__restrict__ newQ)
	A postprocessing routine which pushes the volume solution back into the area of the CCZ4 constraints.

void	enforceCCZ4constraints (const double __restrict__ oldQ, double __restrict__ dQdt, double timeStepSize)
	Anticipate Euler step and correct dQdt such that outcome does fulfill constraints.

void	gaugeWave (double *__restrict__ Q, const tarch::la::Vector< Dimensions, double > &x, double t)

void	diagonal_gaugeWave (double *__restrict__ Q, const tarch::la::Vector< Dimensions, double > &x, double t)

void	linearWave (double *__restrict__ Q, const tarch::la::Vector< Dimensions, double > &X, double t)

void	flat (double *__restrict__ Q, const tarch::la::Vector< Dimensions, double > &X, double t)

void	recomputeAuxiliaryVariablesFD4_4thOrder (::exahype2::CellData< double, double > &patchData, int numberOfGridCellsPerPatchPerAxis, int haloSize, int unknowns, int auxiliaryVariables)
	Recompute auxiliary variables for FD4 scheme with a 4th order scheme.

void	recomputeAuxiliaryVariablesFD4_centralDifferences (::exahype2::CellData< double, double > &patchData, int numberOfGridCellsPerPatchPerAxis, int haloSize, int unknowns, int auxiliaryVariables)

void	recomputeAuxiliaryVariablesFD4_leftDifferences (::exahype2::CellData< double, double > &patchData, int numberOfGridCellsPerPatchPerAxis, int haloSize, int unknowns, int auxiliaryVariables)

void	recomputeAuxiliaryVariablesFD4_rightDifferences (::exahype2::CellData< double, double > &patchData, int numberOfGridCellsPerPatchPerAxis, int haloSize, int unknowns, int auxiliaryVariables)

Function Documentation

◆ admconstraints()

void applications::exahype2::ccz4::admconstraints	(	double *	constraints,
		const double *const	Q,
		const double *const	gradQSerialised )

This is a postprocessing routine to monitor if the physical constraints are fulfilled.

Used in python script.

Definition at line 132 of file CCZ4Kernels.cpp.

References m, tarch::memset(), and u.

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◆ diagonal_gaugeWave()

void applications::exahype2::ccz4::diagonal_gaugeWave	(	double *__restrict__	Q,
		const tarch::la::Vector< Dimensions, double > &	x,
		double	t )

< Amplitude of the wave, B in the note

Definition at line 53 of file InitialValues.cpp.

References H, and tarch::memset().

Referenced by applications::exahype2::ccz4::CCZ4::initialCondition(), applications::exahype2::ccz4::FiniteVolumeCCZ4::initialCondition(), and applications::exahype2::ccz4::RKDGCCZ4::initialCondition().

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◆ enforceCCZ4constraints() [1/2]

void applications::exahype2::ccz4::enforceCCZ4constraints	(	const double *__restrict__	oldQ,
		double *__restrict__	dQdt,
		double	timeStepSize )

Anticipate Euler step and correct dQdt such that outcome does fulfill constraints.

Definition at line 12 of file CCZ4Kernels.cpp.

References enforceCCZ4constraints().

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◆ enforceCCZ4constraints() [2/2]

void applications::exahype2::ccz4::enforceCCZ4constraints ( double *__restrict__ newQ )

A postprocessing routine which pushes the volume solution back into the area of the CCZ4 constraints.

This is a local operation that we can invoke after each time step per volume.

If works on the full set of unknowns of the first-order formulation

Referenced by enforceCCZ4constraints().

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◆ flat()

void applications::exahype2::ccz4::flat	(	double *__restrict__	Q,
		const tarch::la::Vector< Dimensions, double > &	X,
		double	t )

Definition at line 118 of file InitialValues.cpp.

References tarch::memset().

Referenced by applications::exahype2::ccz4::CCZ4::initialCondition(), and applications::exahype2::ccz4::FiniteVolumeCCZ4::initialCondition().

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◆ gaugeWave()

void applications::exahype2::ccz4::gaugeWave	(	double *__restrict__	Q,
		const tarch::la::Vector< Dimensions, double > &	x,
		double	t )

* This file is automatically created by Peano. I need it to interact with
- * the Python API, i.e. to read out data set there.

< Amplitude of the wave

Definition at line 20 of file InitialValues.cpp.

References tarch::memset().

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◆ linearWave()

void applications::exahype2::ccz4::linearWave	(	double *__restrict__	Q,
		const tarch::la::Vector< Dimensions, double > &	X,
		double	t )

< Amplitude of the wave, should be very small to keep linearized.

Definition at line 92 of file InitialValues.cpp.

References tarch::memset().

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◆ maxEigenvalue()

KeywordToAvoidDuplicateSymbolsForInlinedFunctions double applications::exahype2::ccz4::maxEigenvalue	(	const double *const	Q,
		int	normal,
		const double	CCZ4e,
		const double	CCZ4ds,
		const double	CCZ4GLMc,
		const double	CCZ4GLMd )

Todo: Han

Todo: Han

Definition at line 6 of file CCZ4Kernels.cpph.

References std::abs().

Referenced by applications::exahype2::ccz4::CCZ4::maxEigenvalue(), and applications::exahype2::ccz4::FiniteVolumeCCZ4::maxEigenvalue().

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◆ ncp()

KeywordToAvoidDuplicateSymbolsForInlinedFunctions void applications::exahype2::ccz4::ncp	(	double *	BgradQ,
		const double *const	Q,
		const double *const	gradQSerialised,
		const int	normal,
		const int	CCZ4LapseType,
		const double	CCZ4ds,
		const double	CCZ4c,
		const double	CCZ4e,
		const double	CCZ4f,
		const double	CCZ4bs,
		const double	CCZ4sk,
		const double	CCZ4xi,
		const double	CCZ4mu,
		const double	CCZ4SO )

See also: source() for a discussion of annotations.

Definition at line 535 of file CCZ4Kernels.cpph.

References beta, m, temp, and u.

Referenced by exahype2::fd::tests::CCZ4KernelTest::AppleWithAppleTest().

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◆ Psi4Calc()

void applications::exahype2::ccz4::Psi4Calc	(	double *	Psi4,
		const double *const	Q,
		const double *const	gradQSerialised,
		double *	coor )

This function is for the calculation of psi4, a quantity related to gravitional wave.

Not used yet.

Definition at line 376 of file CCZ4Kernels.cpp.

References a, and m.

◆ recomputeAuxiliaryVariablesFD4_4thOrder()

void applications::exahype2::ccz4::recomputeAuxiliaryVariablesFD4_4thOrder	(	::exahype2::CellData< double, double > &	patchData,
		int	numberOfGridCellsPerPatchPerAxis,
		int	haloSize,
		int	unknowns,
		int	auxiliaryVariables )

Recompute auxiliary variables for FD4 scheme with a 4th order scheme.

We are given a patch as well as the number of mesh cells per axis within this patch. I also parameterise over the unknowns and the auxiliaryVariables. By default, we'd expect 59 and 0 here, but we want to routine to work for augmented systems, too.

The reconstruction uses a 4th order Finite Difference scheme. The implementation in applications::exahype2::ccz4::internal::recomputeAuxiliaryVariablesFD4_4thOrder_LoopBody() realises the normal stencil

[1 -8 0 8 -1]

scaled with \( \frac{1}{12h} \). There is a fundamental problem with this variant which is worth mentioning: To evaluate this stencil, we need a halo layer of at least two. For a given haloSize, we can never update the outermost two layers of the code.

Shortcomings

As we use a fourth order scheme, we need two neighbours around each point to construct the outcome. That means, when we are given a patch with size 3 (left illustation above), we effectively can only calculate the auxiliary variables within the patch (green) and the first halo layer around it (brownish). This is illustrated to the right.

There's one further complexity: we usually do not have the digonal values in ExaHyPE. What we really get is not the illustration above to the left but the one in the centre. The diagonal blocks hold garbage. As a consequence, the auxiliary data in the brown data layer to the right is not properly computed. In the left brown layer, only the x-derivatives are properly reconstructed. The y-derivatives contain garbage.

Parameters

patchData	Host the actual patch data. For this function, we only have to ensure that the QIn (data plus halo) are properly set, and that the patch size in patchData is correct. All the other (meta data) properties have no influence and can hold any data.
numberOfGridCellsPerPatchPerAxis	Has to be at least 3, as the halo is also at least three. More general, has to be bigger or equal to haloSize.
haloSize	Has to be at least 3.
unknowns	Typically 59, but can be bigger if you hold additional quantities within the PDE.
auxiliaryVariables	Typically 0.

See also: applications::exahype2::ccz4::internal::recomputeAuxiliaryVariablesFD4_4thOrder_LoopBody()

Definition at line 155 of file SecondOrderAuxiliaryVariablesReconstruction.cpp.

References assertion, exahype2::CellData< inType, outType >::cellCentre, exahype2::CellData< inType, outType >::cellSize, exahype2::CellData< inType, outType >::numberOfCells, and exahype2::CellData< inType, outType >::QIn.

◆ recomputeAuxiliaryVariablesFD4_centralDifferences()

void applications::exahype2::ccz4::recomputeAuxiliaryVariablesFD4_centralDifferences	(	::exahype2::CellData< double, double > &	patchData,
		int	numberOfGridCellsPerPatchPerAxis,
		int	haloSize,
		int	unknowns,
		int	auxiliaryVariables )

Definition at line 104 of file SecondOrderAuxiliaryVariablesReconstruction.cpp.

◆ recomputeAuxiliaryVariablesFD4_leftDifferences()

void applications::exahype2::ccz4::recomputeAuxiliaryVariablesFD4_leftDifferences	(	::exahype2::CellData< double, double > &	patchData,
		int	numberOfGridCellsPerPatchPerAxis,
		int	haloSize,
		int	unknowns,
		int	auxiliaryVariables )

Definition at line 121 of file SecondOrderAuxiliaryVariablesReconstruction.cpp.

◆ recomputeAuxiliaryVariablesFD4_rightDifferences()

void applications::exahype2::ccz4::recomputeAuxiliaryVariablesFD4_rightDifferences	(	::exahype2::CellData< double, double > &	patchData,
		int	numberOfGridCellsPerPatchPerAxis,
		int	haloSize,
		int	unknowns,
		int	auxiliaryVariables )

Definition at line 138 of file SecondOrderAuxiliaryVariablesReconstruction.cpp.

◆ source()

KeywordToAvoidDuplicateSymbolsForInlinedFunctions void applications::exahype2::ccz4::source	(	double *	S,
		const double *const	Q,
		const int	CCZ4LapseType,
		const double	CCZ4ds,
		const double	CCZ4c,
		const double	CCZ4e,
		const double	CCZ4f,
		const double	CCZ4bs,
		const double	CCZ4sk,
		const double	CCZ4xi,
		const double	CCZ4itau,
		const double	CCZ4eta,
		const double	CCZ4k1,
		const double	CCZ4k2,
		const double	CCZ4k3,
		const double	CCZ4SO )

The source term is one out of two terms that we use in our CCZ4 formulation.

As it is used within the compute kernel, we also want to use it on the GPU, and we want to vectorise over it aggressively. To make this work, we have to inline the function plus ensure that the interna of the function are not vectorised before we inline the routine.

So we first declare it as simd and then we also say explicitly that it should be inlined. In my opinion, the inlining should imply that we wanna use it as SIMD, but my guess is that the simd statement ensures that the compiler doesn't prematurely vectorise.

See also: ncp()

Main variables of the CCZ4 system

Definition at line 25 of file CCZ4Kernels.cpph.

References beta, m, temp, and u.

Referenced by exahype2::fd::tests::CCZ4KernelTest::AppleWithAppleTest(), applications::exahype2::ccz4::internal::recomputeAuxiliaryVariablesFD4_centralDifferences_LoopBody(), applications::exahype2::ccz4::internal::recomputeAuxiliaryVariablesFD4_leftDifferences_LoopBody(), applications::exahype2::ccz4::internal::recomputeAuxiliaryVariablesFD4_rightDifferences_LoopBody(), applications::exahype2::ccz4::CCZ4::sourceTerm(), applications::exahype2::ccz4::FiniteVolumeCCZ4::sourceTerm(), and benchmarks::exahype2::ccz4::CCZ4::sourceTerm().

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◆ TestingOutput()

void applications::exahype2::ccz4::TestingOutput	(	double *	terms,
		const double *const	Q,
		const double *const	gradQSerialised )

A temporary test function, to output some testing values 0,1 entries: Hamilton constraint related term in theta, 2 terms: RPlusTwoNablaZSrc, pure Src 2-10 entry: no-symmetry version of R_ij.

Definition at line 678 of file CCZ4Kernels.cpp.

References m, tarch::memset(), temp, and u.

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◆ ThetaOutputNCP()

void applications::exahype2::ccz4::ThetaOutputNCP	(	double *	NCPterm,
		const double *const	Q,
		const double *const	gradQSerialised,
		int	normal )

A temporary test function, to output Hamilton constraint related term in theta, 1 terms: RPlusTwoNablaZNCP.

Definition at line 955 of file CCZ4Kernels.cpp.

References m, and u.

Namespaces

Data Structures

Functions

Function Documentation

◆ admconstraints()

◆ diagonal_gaugeWave()

◆ enforceCCZ4constraints() [1/2]

◆ enforceCCZ4constraints() [2/2]

◆ flat()

◆ gaugeWave()

◆ linearWave()

◆ maxEigenvalue()

◆ ncp()

◆ Psi4Calc()

◆ recomputeAuxiliaryVariablesFD4_4thOrder()

Shortcomings

◆ recomputeAuxiliaryVariablesFD4_centralDifferences()

◆ recomputeAuxiliaryVariablesFD4_leftDifferences()

◆ recomputeAuxiliaryVariablesFD4_rightDifferences()

◆ source()

◆ TestingOutput()

◆ ThetaOutputNCP()