Constraints

Description

Utilities for handling affine constraints.

Classes
class	Dune::Fufem::AffineConstraints< BV, V, MI, C >
	Class to handle affine constraints on a subset of DOFs. More...

Functions
template<class BitVector = std::monostate, class Vector = std::monostate, class Basis >
auto	Dune::Fufem::makeAffineConstraints (const Basis &basis)
	Create and initialize an AffineConstraints object for a basis.
template<class BV , class V , class MI , class C , class Basis , class Function , class IntersectionSet > requires (Dune::Fufem::Forms::IsBoundaryDomain<IntersectionSet>::value or Dune::Fufem::Forms::IsSkeletonDomain<IntersectionSet>::value)
void	Dune::Fufem::computeBoundaryConstraints (AffineConstraints< BV, V, MI, C > &constraints, const Basis &basis, Function &&f, const IntersectionSet &intersectionSet)
	Compute constraints for essential boundary conditions.
template<class BV , class V , class MI , class C , class Basis , class Function >
void	Dune::Fufem::computeBoundaryConstraints (AffineConstraints< BV, V, MI, C > &constraints, const Basis &basis, Function &&f)
	Compute constraints for essential boundary conditions.
template<class BitVector = std::monostate, class Vector = std::monostate, class Basis , class Function , class IntersectionSet > requires (Dune::Fufem::Forms::IsBoundaryDomain<IntersectionSet>::value or Dune::Fufem::Forms::IsSkeletonDomain<IntersectionSet>::value)
auto	Dune::Fufem::makeBoundaryConstraints (const Basis &basis, Function &&f, const IntersectionSet &intersectionSet)
	Compute constraints for essential boundary conditions.
template<class BitVector = std::monostate, class Vector = std::monostate, class Basis , class Function >
auto	Dune::Fufem::makeBoundaryConstraints (const Basis &basis, Function &&f)
	Compute constraints for essential boundary conditions.
template<class BV , class V , class MI , class C , class Basis >
void	Dune::Fufem::computeContinuityConstraints (AffineConstraints< BV, V, MI, C > &constraints, const Basis &basis)
	Compute constraints for a conforming basis on a grid with hanging nodes.
template<class BitVector = std::monostate, class Vector = std::monostate, class Basis >
auto	Dune::Fufem::makeContinuityConstraints (const Basis &basis)
	Compute constraints for a conforming basis on a grid with hanging nodes.
template<class PrimaryLocalView , class SecondaryLocalView , class SecondaryToPrimary , class SecondaryDOFs , class Constraints >
void	Dune::Fufem::computeLocalInterpolationConstraints (const PrimaryLocalView &primaryLocalView, const SecondaryLocalView &secondaryLocalView, const SecondaryToPrimary &localSecondaryToPrimary, const SecondaryDOFs &secondaryDOFs, Constraints &constraints)
	Compute local constraints from interpolating between local views.
template<class BV , class V , class MI , class C , class PrimaryBasis , class PrimaryPatch , class SecondaryBasis , class SecondaryPatch , class SecondaryToPrimary >
void	Dune::Fufem::computePeriodicConstraints (AffineConstraints< BV, V, MI, C > &constraints, const PrimaryBasis &primaryBasis, const PrimaryPatch &primaryPatch, const SecondaryBasis &secondaryBasis, const SecondaryPatch &secondaryPatch, const SecondaryToPrimary &secondaryToPrimary)
	Compute constraints for periodic boundary conditions.
template<class BV , class V , class MI , class C , class Basis , class PrimaryPatch , class SecondaryPatch , class SecondaryToPrimary >
void	Dune::Fufem::computePeriodicConstraints (AffineConstraints< BV, V, MI, C > &constraints, const Basis &basis, const PrimaryPatch &primaryPatch, const SecondaryPatch &secondaryPatch, const SecondaryToPrimary &secondaryToPrimary)
	Compute constraints for periodic boundary conditions.

Function Documentation

computeBoundaryConstraints() [1/2]

template<class BV , class V , class MI , class C , class Basis , class Function >

void Dune::Fufem::computeBoundaryConstraints	(	AffineConstraints< BV, V, MI, C > &	constraints,
		const Basis &	basis,
		Function &&	f
	)

Compute constraints for essential boundary conditions.

Template Parameters

Basis	Type of the global basis
Function	Type of the function to interpolate

Parameters

constraints	An initialized AffineConstraints object
basis	A global basis
f	The Dirichlet values given as a function

This will interpolate the function f on the whole boundary and add constraints for all corresponding DOFs to constraints.

Note

This method assumes that the constraints has already been initialized. If constraints already contains constraint DOFs, then interpolation and the newly added constraints are reduced to the previously unconstrained DOFs.

Warning

This function is still experimental and the interface may change.

computeBoundaryConstraints() [2/2]

template<class BV , class V , class MI , class C , class Basis , class Function , class IntersectionSet >
requires (Dune::Fufem::Forms::IsBoundaryDomain<IntersectionSet>::value or Dune::Fufem::Forms::IsSkeletonDomain<IntersectionSet>::value)

void Dune::Fufem::computeBoundaryConstraints	(	AffineConstraints< BV, V, MI, C > &	constraints,
		const Basis &	basis,
		Function &&	f,
		const IntersectionSet &	intersectionSet
	)

Compute constraints for essential boundary conditions.

Template Parameters

Basis	Type of the global basis
Function	Type of the function to interpolate
IntersectionSet	Type of IntersectionSet. This should satisfy Forms::IsBoundaryDomain or Forms::IsSkeletonDomain. This is e.g. the case for BoundaryPatch and Forms::Boundary.

Parameters

constraints	An initialized AffineConstraints object
basis	A global basis
f	The Dirichlet values given as a function
intersectionSet	The IntersectionSet where the boundary condition should be applied

This will interpolate the function f on the intersectionSet and add constraints for all corresponding DOFs to constraints.

Note

This method assumes that the constraints has already been initialized. If constraints already contains constraint DOFs, then interpolation and the newly added constraints are reduced to the previously unconstrained DOFs.

Warning

This function is still experimental and the interface may change.

computeContinuityConstraints()

template<class BV , class V , class MI , class C , class Basis >

void Dune::Fufem::computeContinuityConstraints	(	AffineConstraints< BV, V, MI, C > &	constraints,
		const Basis &	basis
	)

Compute constraints for a conforming basis on a grid with hanging nodes.

Template Parameters

Basis

Type of the global basis

Parameters

constraints	An initialized AffineConstraints object
basis	A global basis

This will compute the constraints required to get a basis for the subspace of continuous functions. This method is intended to be used for getting the \(H^1\)-conforming subspace of a finite element space on a grid with hanging nodes. It assumes that DOFs for noncontinuous basis functions on an element can be interpolated from basis functions of neighboring elements on coarser levels.

Note

This method assumes that the AffineConstraints object constraints has already been initialized. It may also already contain constraints.

Warning

This function is still experimental and the interface may change.

computeLocalInterpolationConstraints()

template<class PrimaryLocalView , class SecondaryLocalView , class SecondaryToPrimary , class SecondaryDOFs , class Constraints >

void Dune::Fufem::computeLocalInterpolationConstraints	(	const PrimaryLocalView &	primaryLocalView,
		const SecondaryLocalView &	secondaryLocalView,
		const SecondaryToPrimary &	localSecondaryToPrimary,
		const SecondaryDOFs &	secondaryDOFs,
		Constraints &	constraints
	)

Compute local constraints from interpolating between local views.

Template Parameters

Basis

Type of the global basis

Parameters

primaryLocalView	The primary local view
secondaryLocalView	The secondary local view
localSecondaryToPrimary	Callback mapping local coordinates
secondaryDOFs	A set of local DOFs to be interpolated
constraints	An initialized AffineConstraints object that will be modified

For the given pair of local views the DOFs from the secondaryLocalView contained in the secondaryDOFs container are interpolated from the DOFs of the primaryLocalView. The secondary boundary face DOFs are marked as constrained and the interpolation weights are used as constraint weights.

The secondaryDOFs container must support secondaryDOFs.contains(secondaryLocalIndex).

Note

This function is primarily intended to be used inside of other functions computing global constraints, like, e.g. periodic or hanging node constraints.

Warning

This function is still experimental and the interface may change.

computePeriodicConstraints() [1/2]

template<class BV , class V , class MI , class C , class Basis , class PrimaryPatch , class SecondaryPatch , class SecondaryToPrimary >

void Dune::Fufem::computePeriodicConstraints	(	AffineConstraints< BV, V, MI, C > &	constraints,
		const Basis &	basis,
		const PrimaryPatch &	primaryPatch,
		const SecondaryPatch &	secondaryPatch,
		const SecondaryToPrimary &	secondaryToPrimary
	)

Compute constraints for periodic boundary conditions.

Template Parameters

Basis	Type of the global basis
PrimaryPatch	Type of BoundaryPatch (or intersection range) for the primary periodic boundary
SecondaryPatch	Type of BoundaryPatch (or intersection range) for the secondary periodic boundary
SecondaryToPrimary	Type of boundary-to-boundary map

Parameters

constraints	An initialized AffineConstraints object
basis	A global basis
primaryPatch	The patch containing the primary part of the periodic boundary
secondaryPatch	The patch containing the secondary part of the periodic boundary
secondaryToPrimary	A function mapping coordinates from the secondary to primary boundary

This will first search matching pairs of boundary faces from the primaryPatch and secondaryPatch. A pair of faces is considered of match if the center of the secondary boundary face mapped to the primary boundary coincides (up to a tolerance) with the center of the primary boundary face. The mapping is done by the callback secondaryToPrimary.

For any matching pair the DOFs associated to the secondary boundary face are then interpolated from the DOFs on the primary boundary face. The secondary boundary face DOFs are marked as constrained and the interpolation weights are used as constraint weights.

Note

This method assumes that the constraints has already been initialized. If constraints already contains constraint DOFs, then the newly added constraints are reduced to the previously unconstrained DOFs.

Warning

This function is still experimental and the interface may change.

computePeriodicConstraints() [2/2]

template<class BV , class V , class MI , class C , class PrimaryBasis , class PrimaryPatch , class SecondaryBasis , class SecondaryPatch , class SecondaryToPrimary >

void Dune::Fufem::computePeriodicConstraints	(	AffineConstraints< BV, V, MI, C > &	constraints,
		const PrimaryBasis &	primaryBasis,
		const PrimaryPatch &	primaryPatch,
		const SecondaryBasis &	secondaryBasis,
		const SecondaryPatch &	secondaryPatch,
		const SecondaryToPrimary &	secondaryToPrimary
	)

Compute constraints for periodic boundary conditions.

Template Parameters

PrimaryBasis	Type of the primary global basis
PrimaryPatch	Type of BoundaryPatch (or intersection range) for the primary periodic boundary
SecondaryBasis	Type of the secondary global basis
SecondaryPatch	Type of BoundaryPatch (or intersection range) for the secondary periodic boundary
SecondaryToPrimary	Type of boundary-to-boundary map

Parameters

constraints	An initialized AffineConstraints object
primaryBasis	A global basis to be considered on the primary boundary
primaryPatch	The patch containing the primary part of the periodic boundary
secondaryBasis	A global basis to be considered on the secondary boundary
secondaryPatch	The patch containing the secondary part of the periodic boundary
secondaryToPrimary	A function mapping coordinates from the secondary to primary boundary

This will first search matching pairs of boundary faces from the primaryPatch and secondaryPatch. A pair of faces is considered of match if the center of the secondary boundary face mapped to the primary boundary coincides (up to a tolerance) with the center of the primary boundary face. The mapping is done by the callback secondaryToPrimary.

For any matching pair the secondary basis DOFs associated to the secondary boundary face are then interpolated from the primary basis DOFs on the primary boundary face. The secondary boundary face DOFs are marked as constrained and the interpolation weights are used as constraint weights.

Note

This method assumes that the constraints has already been initialized. If constraints already contains constraint DOFs, then the newly added constraints are reduced to the previously unconstrained DOFs.

Warning

This function is still experimental and the interface may change.

makeAffineConstraints()

template<class BitVector = std::monostate, class Vector = std::monostate, class Basis >

auto Dune::Fufem::makeAffineConstraints

(

const Basis &

basis

)

Create and initialize an AffineConstraints object for a basis.

Template Parameters

BitVector	A bit vector type suitable for the global indices of the basis
Vector	A coefficient vector type suitable for the global indices of the basis
Basis	Type of the global basis

Parameters

basis

A global basis

If the template default value std::monostate is used for the template parameters BitVector or Vector then the actual container types are deduced using Dune::Functions::makeContainer(...) and Dune::Functions::makeISTLVector(...) from the container descriptor provided by basis (only with dune-function>=2.11).

makeBoundaryConstraints() [1/2]

template<class BitVector = std::monostate, class Vector = std::monostate, class Basis , class Function >

auto Dune::Fufem::makeBoundaryConstraints	(	const Basis &	basis,
		Function &&	f
	)

Compute constraints for essential boundary conditions.

Template Parameters

BitVector	A bit vector type suitable for the global indices of the basis
Vector	A coefficient vector type suitable for the global indices of the basis
Basis	Type of the global basis
Function	Type of the function to interpolate

Parameters

basis	A global basis
f	The Dirichlet values given as a function

This will interpolate the function f on the boundary and return an AffineConstraints object constraining all corresponding DOFs.

If the template default value std::monostate is used for the template parameters BitVector or Vector then the actual container types are deduced using Dune::Functions::makeContainer(...) and Dune::Functions::makeISTLVector(...) from the container descriptor provided by basis (only with dune-function>=2.11).

Warning

This function is still experimental and the interface may change.

makeBoundaryConstraints() [2/2]

template<class BitVector = std::monostate, class Vector = std::monostate, class Basis , class Function , class IntersectionSet >
requires (Dune::Fufem::Forms::IsBoundaryDomain<IntersectionSet>::value or Dune::Fufem::Forms::IsSkeletonDomain<IntersectionSet>::value)

auto Dune::Fufem::makeBoundaryConstraints	(	const Basis &	basis,
		Function &&	f,
		const IntersectionSet &	intersectionSet
	)

Compute constraints for essential boundary conditions.

Template Parameters

BitVector	A bit vector type suitable for the global indices of the basis
Vector	A coefficient vector type suitable for the global indices of the basis
Basis	Type of the global basis
Function	Type of the function to interpolate
IntersectionSet	Type of IntersectionSet. This should satisfy Forms::IsBoundaryDomain or Forms::IsSkeletonDomain. This is e.g. the case for BoundaryPatch and Forms::Boundary.

Parameters

basis	A global basis
f	The Dirichlet values given as a function
intersectionSet	The IntersectionSet where the boundary condition should be applied

This will interpolate the function f on the intersectionSet and return an AffineConstraints object constraining all corresponding DOFs.

If the template default value std::monostate is used for the template parameters BitVector or Vector then the actual container types are deduced using Dune::Functions::makeContainer(...) and Dune::Functions::makeISTLVector(...) from the container descriptor provided by basis (only with dune-function>=2.11).

Warning

This function is still experimental and the interface may change.

makeContinuityConstraints()

template<class BitVector = std::monostate, class Vector = std::monostate, class Basis >

auto Dune::Fufem::makeContinuityConstraints

(

const Basis &

basis

)

Compute constraints for a conforming basis on a grid with hanging nodes.

Template Parameters

BitVector	A bit vector type suitable for the global indices of the basis
Vector	A coefficient vector type suitable for the global indices of the basis
Basis	Type of the global basis

Parameters

basis

A global basis

This will compute the constraints required to get a basis for the subspace of continuous functions. This method is intended to be used for getting the \(H^1\)-conforming subspace of a finite element space on a grid with hanging nodes. It assumes that DOFs for noncontinuous basis functions on an element can be interpolated from basis functions of neighboring elements on coarser levels.

The constraints are returned as AffineConstraints object. The result can be used to constrain a linear system to the conforming subspace.

If the template default value std::monostate is used for the template parameters BitVector or Vector then the actual container types are deduced using Dune::Functions::makeContainer(...) and Dune::Functions::makeISTLVector(...) from the container descriptor provided by basis (only with dune-function>=2.11).

Warning

This function is still experimental and the interface may change.