Class for subdomain IntegrationRules by means of moment-fitting. More...

#include <intrules_cut.hpp>

Inheritance diagram for mfem::MomentFittingIntRules:

Collaboration diagram for mfem::MomentFittingIntRules:

Public Member Functions
	MomentFittingIntRules (int order, Coefficient &lvlset, int lsO)
	Constructor to set up the generated cut IntegrationRules.

void	SetOrder (int order) override
	Change the order of the constructed IntegrationRule.

void	GetSurfaceIntegrationRule (ElementTransformation &Tr, IntegrationRule &result) override
	Construct a cut-surface IntegrationRule.

void	GetVolumeIntegrationRule (ElementTransformation &Tr, IntegrationRule &result, const IntegrationRule *sir=nullptr) override
	Construct a cut-volume IntegrationRule.

void	GetSurfaceWeights (ElementTransformation &Tr, const IntegrationRule &sir, Vector &weights) override
	Compute transformation quadrature weights for surface integration.

	~MomentFittingIntRules () override
	Destructor of MomentFittingIntRules.

virtual void	SetLevelSetCoefficient (Coefficient &ls)
	Change the Coefficient whose zero level set specifies the cut.

virtual void	SetLevelSetProjectionOrder (int order)

Public Member Functions inherited from mfem::CutIntegrationRules
virtual	~CutIntegrationRules ()
	Destructor of CutIntegrationRules.

Protected Member Functions
void	InitSurface (int order, Coefficient &levelset, int lsO, ElementTransformation &Tr)
	Initialization for surface IntegrationRule.

void	InitVolume (int order, Coefficient &levelset, int lsO, ElementTransformation &Tr)
	Initialization for volume IntegrationRule.

void	Init (int order, Coefficient &levelset, int lsO)
	Initialize the MomentFittingIntRules.

void	Clear ()
	Clear stored data of the MomentFittingIntRules.

void	ComputeFaceWeights (ElementTransformation &Tr)
	Compute the IntegrationRules on the faces.

void	ComputeSurfaceWeights1D (ElementTransformation &Tr)
	Compute 1D quadrature weights.

void	ComputeVolumeWeights1D (ElementTransformation &Tr)
	Compute the 1D quadrature weights.

void	ComputeSurfaceWeights2D (ElementTransformation &Tr)
	Compute 2D quadrature weights.

void	ComputeVolumeWeights2D (ElementTransformation &Tr, const IntegrationRule *sir)
	Compute the 2D quadrature weights.

void	ComputeSurfaceWeights3D (ElementTransformation &Tr)
	Compute 2D quadrature weights.

void	ComputeVolumeWeights3D (ElementTransformation &Tr, const IntegrationRule *sir)
	Compute the 3D quadrature weights.

void	DivFreeBasis2D (const IntegrationPoint &ip, DenseMatrix &shape)
	A divergence free basis on the element [-1,1]^2.

void	OrthoBasis2D (const IntegrationPoint &ip, DenseMatrix &shape)
	A orthogonalized divergence free basis on the element [-1,1]^2.

void	OrthoBasis3D (const IntegrationPoint &ip, DenseMatrix &shape)
	A orthogonalized divergence free basis on the element [-1,1]^3.

void	mGSStep (DenseMatrix &shape, DenseTensor &shapeMFN, int step)
	A step of the modified Gram-Schmidt algorithm.

void	Basis2D (const IntegrationPoint &ip, Vector &shape)
	Monomial basis on the element [-1,1]^2.

void	BasisAD2D (const IntegrationPoint &ip, DenseMatrix &shape)
	Antiderivatives of the monomial basis on the element [-1,1]^2.

void	Basis3D (const IntegrationPoint &ip, Vector &shape)
	Monomial basis on the element [-1,1]^3.

void	BasisAD3D (const IntegrationPoint &ip, DenseMatrix &shape)
	Antiderivatives of the monomial basis on the element [-1,1]^3.

Protected Member Functions inherited from mfem::CutIntegrationRules
	CutIntegrationRules (int order, Coefficient &lvlset, int lsO=2)
	Constructor to set up the generated cut IntegrationRules.

Protected Attributes
int	dim
	Space Dimension of the element.

int	nBasis
	Number of divergence-free basis functions for surface integration.

int	nBasisVolume
	Number of basis functions for volume integration.

IntegrationRule	ir
	IntegrationRule representing the reused IntegrationPoints.

DenseMatrixSVD *	VolumeSVD
	SVD of the matrix for volumetric IntegrationRules.

Array< IntegrationPoint >	FaceIP
	Array of face integration points.

DenseMatrix	FaceWeights
	Column-wise Matrix for the face quadrature weights.

Vector	FaceWeightsComp
	Indicates the already computed face IntegrationRules.

Protected Attributes inherited from mfem::CutIntegrationRules
int	Order
	Order of the IntegrationRule.

Coefficient *	LvlSet
	The zero level set of this Coefficient defines the cut surface.

int	lsOrder
	Space order for the LS projection.

Additional Inherited Members
Static Protected Attributes inherited from mfem::CutIntegrationRules
static constexpr real_t	tol_1 = 1e-12

static constexpr real_t	tol_2 = 1e-15

Detailed Description

Class for subdomain IntegrationRules by means of moment-fitting.

Class for subdomain (surface and subdomain) IntegrationRules by means of moment-fitting. The class provides different functions to construct the IntegrationRules. The construction is done as described in Mueller et al. in "Highly accurate surface and volume integration on implicit domains by means of moment-fitting" (2013, see https://onlinelibrary.wiley.com/doi/full/10.1002/nme.4569).

Definition at line 484 of file intrules_cut.hpp.

Constructor & Destructor Documentation

◆ MomentFittingIntRules()

mfem::MomentFittingIntRules::MomentFittingIntRules	(	int	order,
		Coefficient &	lvlset,
		int	lsO )

inline

Constructor to set up the generated cut IntegrationRules.

Parameters

[in]	order	Order of the constructed IntegrationRule.
[in]	lvlset	Coefficient whose zero level set specifies the cut.
[in]	lsO	Polynomial degree for projecting the level-set Coefficient to a GridFunction, which is used to compute gradients and normals.

Definition at line 651 of file intrules_cut.hpp.

◆ ~MomentFittingIntRules()

mfem::MomentFittingIntRules::~MomentFittingIntRules ( )

inlineoverride

Destructor of MomentFittingIntRules.

Definition at line 705 of file intrules_cut.hpp.

Member Function Documentation

◆ Basis2D()

void mfem::MomentFittingIntRules::Basis2D	(	const IntegrationPoint &	ip,
		Vector &	shape )

protected

Monomial basis on the element [-1,1]^2.

Definition at line 1535 of file intrules_cut.cpp.

◆ Basis3D()

void mfem::MomentFittingIntRules::Basis3D	(	const IntegrationPoint &	ip,
		Vector &	shape )

protected

Monomial basis on the element [-1,1]^3.

Definition at line 1580 of file intrules_cut.cpp.

◆ BasisAD2D()

void mfem::MomentFittingIntRules::BasisAD2D	(	const IntegrationPoint &	ip,
		DenseMatrix &	shape )

protected

Antiderivatives of the monomial basis on the element [-1,1]^2.

Definition at line 1555 of file intrules_cut.cpp.

◆ BasisAD3D()

void mfem::MomentFittingIntRules::BasisAD3D	(	const IntegrationPoint &	ip,
		DenseMatrix &	shape )

protected

Antiderivatives of the monomial basis on the element [-1,1]^3.

Definition at line 1601 of file intrules_cut.cpp.

◆ Clear()

void mfem::MomentFittingIntRules::Clear ( )

protected

Clear stored data of the MomentFittingIntRules.

Definition at line 1632 of file intrules_cut.cpp.

◆ ComputeFaceWeights()

void mfem::MomentFittingIntRules::ComputeFaceWeights ( ElementTransformation & Tr )

protected

Compute the IntegrationRules on the faces.

Compute the IntegrationRules on the (cut) faces of an element. These will be saved and reused if possible.

Parameters

[in] Tr ElementTransformation of the element the IntegrationRules on the faces are computed

Definition at line 294 of file intrules_cut.cpp.

◆ ComputeSurfaceWeights1D()

void mfem::MomentFittingIntRules::ComputeSurfaceWeights1D ( ElementTransformation & Tr )

protected

Compute 1D quadrature weights.

Compute the quadrature weights for the 1D surface quadrature rule.

Parameters

[in] Tr ElementTransformation of the current element

Definition at line 377 of file intrules_cut.cpp.

◆ ComputeSurfaceWeights2D()

void mfem::MomentFittingIntRules::ComputeSurfaceWeights2D ( ElementTransformation & Tr )

protected

Compute 2D quadrature weights.

Compute the quadrature weights for the 2D surface quadrature rule by means of moment-fitting. To construct the quadrature rule, special integrals are reduced to integrals over the edges of the subcell where the level-set is positive.

Parameters

[in] Tr ElementTransformation of the current element

Definition at line 524 of file intrules_cut.cpp.

◆ ComputeSurfaceWeights3D()

void mfem::MomentFittingIntRules::ComputeSurfaceWeights3D ( ElementTransformation & Tr )

protected

Compute 2D quadrature weights.

Compute the quadrature weights for the 3D surface quadrature rule by means of moment-fitting. To construct the quadrature rule, special integrals are reduced to integrals over the edges of the subcell where the level-set is positive.

Parameters

[in] Tr ElementTransformation of the current element

Definition at line 1033 of file intrules_cut.cpp.

◆ ComputeVolumeWeights1D()

void mfem::MomentFittingIntRules::ComputeVolumeWeights1D ( ElementTransformation & Tr )

protected

Compute the 1D quadrature weights.

Compute the 1D quadrature weights for the volumetric subdomain quadrature rule.

Parameters

[in] Tr ElementTransformation of the current element

Definition at line 473 of file intrules_cut.cpp.

◆ ComputeVolumeWeights2D()

void mfem::MomentFittingIntRules::ComputeVolumeWeights2D	(	ElementTransformation &	Tr,
		const IntegrationRule *	sir )

protected

Compute the 2D quadrature weights.

Compute the 2D quadrature weights for the volumetric subdomain quadrature rule by means of moment-fitting. To construct the quadrature rule, special integrals are reduced to integrals over the boundary of the subcell where the level-set is positive.

Parameters

[in]	Tr	ElementTransformation of the current element
[in]	sir	corresponding IntegrationRule on surface

Definition at line 775 of file intrules_cut.cpp.

◆ ComputeVolumeWeights3D()

void mfem::MomentFittingIntRules::ComputeVolumeWeights3D	(	ElementTransformation &	Tr,
		const IntegrationRule *	sir )

protected

Compute the 3D quadrature weights.

Compute the 3D quadrature weights for the volumetric subdomain quadrature rule by means of moment-fitting. To construct the quadrature rule, special integrals are reduced to integrals over the boundary of the subcell where the level-set is positive.

Parameters

[in]	Tr	ElementTransformation of the current element
[in]	sir	corresponding IntegrationRule on surface

Definition at line 1214 of file intrules_cut.cpp.

◆ DivFreeBasis2D()

void mfem::MomentFittingIntRules::DivFreeBasis2D	(	const IntegrationPoint &	ip,
		DenseMatrix &	shape )

protected

A divergence free basis on the element [-1,1]^2.

Definition at line 1407 of file intrules_cut.cpp.

◆ GetSurfaceIntegrationRule()

void mfem::MomentFittingIntRules::GetSurfaceIntegrationRule	(	ElementTransformation &	Tr,
		IntegrationRule &	result )

overridevirtual

Construct a cut-surface IntegrationRule.

Construct an IntegrationRule to integrate on the surface given by the already specified level set function, for the element given by Tr.

Parameters

[in]	Tr	Specifies the IntegrationRule's associated mesh element.
[out]	result	IntegrationRule on the cut-surface

Implements mfem::CutIntegrationRules.

Definition at line 1650 of file intrules_cut.cpp.

◆ GetSurfaceWeights()

void mfem::MomentFittingIntRules::GetSurfaceWeights	(	ElementTransformation &	Tr,
		const IntegrationRule &	sir,
		Vector &	weights )

overridevirtual

Compute transformation quadrature weights for surface integration.

Compute the transformation weights for integration over the cut-surface in reference space.

Parameters

[in]	Tr	Specifies the IntegrationRule's associated element.
[in]	sir	IntegrationRule defining the IntegrationPoints
[out]	weights	Vector containing the transformation weights.

Implements mfem::CutIntegrationRules.

Definition at line 1754 of file intrules_cut.cpp.

◆ GetVolumeIntegrationRule()

void mfem::MomentFittingIntRules::GetVolumeIntegrationRule	(	ElementTransformation &	Tr,
		IntegrationRule &	result,
		const IntegrationRule *	sir = nullptr )

overridevirtual

Construct a cut-volume IntegrationRule.

Construct an IntegrationRule to integrate in the subdomain given by the positive values of the already specified level set function, for the element given by Tr.

Parameters

[in]	Tr	Specifies the IntegrationRule's associated mesh element.
[out]	result	IntegrationRule for the cut-volume
[in]	sir	Corresponding IntegrationRule for the surface, which can be used to avoid computations.

Implements mfem::CutIntegrationRules.

Definition at line 1691 of file intrules_cut.cpp.

◆ Init()

void mfem::MomentFittingIntRules::Init	(	int	order,
		Coefficient &	levelset,
		int	lsO )

inlineprotected

Initialize the MomentFittingIntRules.

Definition at line 535 of file intrules_cut.hpp.

◆ InitSurface()

void mfem::MomentFittingIntRules::InitSurface	(	int	order,
		Coefficient &	levelset,
		int	lsO,
		ElementTransformation &	Tr )

protected

Initialization for surface IntegrationRule.

Initialize the members for computation of surface IntegrationRule. This is called when the first IntegrationRule is computed or when Order or level-set change.

Parameters

[in]	order	Order of the IntegrationRule
[in]	levelset	level-set function defining the implicit interface
[in]	lsO	polynomial degree for approximation of level-set function
[in]	Tr	ElemenTransformation to initalize the members with

Definition at line 202 of file intrules_cut.cpp.

◆ InitVolume()

void mfem::MomentFittingIntRules::InitVolume	(	int	order,
		Coefficient &	levelset,
		int	lsO,
		ElementTransformation &	Tr )

protected

Initialization for volume IntegrationRule.

Initialize the members for computation of surface IntegrationRule. This is called when the first IntegrationRule is computed or when Order or level-set change.

Parameters

[in]	order	Order of the IntegrationRule
[in]	levelset	level-set function defining the implicit interface
[in]	lsO	polynomial degree for approximation of level-set function
[in]	Tr	ElemenTransformation to initalize the members with

Definition at line 242 of file intrules_cut.cpp.

◆ mGSStep()

void mfem::MomentFittingIntRules::mGSStep	(	DenseMatrix &	shape,
		DenseTensor &	shapeMFN,
		int	step )

protected

A step of the modified Gram-Schmidt algorithm.

Definition at line 1492 of file intrules_cut.cpp.

◆ OrthoBasis2D()

void mfem::MomentFittingIntRules::OrthoBasis2D	(	const IntegrationPoint &	ip,
		DenseMatrix &	shape )

protected

A orthogonalized divergence free basis on the element [-1,1]^2.

Definition at line 1450 of file intrules_cut.cpp.

◆ OrthoBasis3D()

void mfem::MomentFittingIntRules::OrthoBasis3D	(	const IntegrationPoint &	ip,
		DenseMatrix &	shape )

protected

A orthogonalized divergence free basis on the element [-1,1]^3.

Definition at line 1481 of file intrules_cut.cpp.

◆ SetLevelSetCoefficient()

virtual void mfem::CutIntegrationRules::SetLevelSetCoefficient ( Coefficient & ls )

inlinevirtual

Change the Coefficient whose zero level set specifies the cut.

Reimplemented from mfem::CutIntegrationRules.

Definition at line 77 of file intrules_cut.hpp.

◆ SetLevelSetProjectionOrder()

void mfem::CutIntegrationRules::SetLevelSetProjectionOrder ( int order )

virtual

Change the polynomial degree for projecting the level set Coefficient to a GridFunction, which is used to compute local gradients and normals.

Reimplemented from mfem::CutIntegrationRules.

Definition at line 81 of file intrules_cut.cpp.

◆ SetOrder()

void mfem::MomentFittingIntRules::SetOrder ( int order )

overridevirtual

Change the order of the constructed IntegrationRule.

Reimplemented from mfem::CutIntegrationRules.

Definition at line 1644 of file intrules_cut.cpp.

Member Data Documentation

◆ dim

int mfem::MomentFittingIntRules::dim

protected

Space Dimension of the element.

Definition at line 488 of file intrules_cut.hpp.

◆ FaceIP

Array<IntegrationPoint> mfem::MomentFittingIntRules::FaceIP

protected

Array of face integration points.

Definition at line 498 of file intrules_cut.hpp.

◆ FaceWeights

DenseMatrix mfem::MomentFittingIntRules::FaceWeights

protected

Column-wise Matrix for the face quadrature weights.

Definition at line 500 of file intrules_cut.hpp.

◆ FaceWeightsComp

Vector mfem::MomentFittingIntRules::FaceWeightsComp

protected

Indicates the already computed face IntegrationRules.

Definition at line 502 of file intrules_cut.hpp.

◆ ir

IntegrationRule mfem::MomentFittingIntRules::ir

protected

IntegrationRule representing the reused IntegrationPoints.

Definition at line 494 of file intrules_cut.hpp.

◆ nBasis

int mfem::MomentFittingIntRules::nBasis

protected

Number of divergence-free basis functions for surface integration.

Definition at line 490 of file intrules_cut.hpp.

◆ nBasisVolume

int mfem::MomentFittingIntRules::nBasisVolume

protected

Number of basis functions for volume integration.

Definition at line 492 of file intrules_cut.hpp.

◆ VolumeSVD

DenseMatrixSVD* mfem::MomentFittingIntRules::VolumeSVD

protected

SVD of the matrix for volumetric IntegrationRules.

Definition at line 496 of file intrules_cut.hpp.

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

fem/intrules_cut.hpp
fem/intrules_cut.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ MomentFittingIntRules()

◆ ~MomentFittingIntRules()

Member Function Documentation

◆ Basis2D()

◆ Basis3D()

◆ BasisAD2D()

◆ BasisAD3D()

◆ Clear()

◆ ComputeFaceWeights()

◆ ComputeSurfaceWeights1D()

◆ ComputeSurfaceWeights2D()

◆ ComputeSurfaceWeights3D()

◆ ComputeVolumeWeights1D()

◆ ComputeVolumeWeights2D()

◆ ComputeVolumeWeights3D()

◆ DivFreeBasis2D()

◆ GetSurfaceIntegrationRule()

◆ GetSurfaceWeights()

◆ GetVolumeIntegrationRule()

◆ Init()

◆ InitSurface()

◆ InitVolume()

◆ mGSStep()

◆ OrthoBasis2D()

◆ OrthoBasis3D()

◆ SetLevelSetCoefficient()

◆ SetLevelSetProjectionOrder()

◆ SetOrder()

Member Data Documentation

◆ dim

◆ FaceIP

◆ FaceWeights

◆ FaceWeightsComp

◆ ir

◆ nBasis

◆ nBasisVolume

◆ VolumeSVD