Class FiniteElementSpace - responsible for providing FEM view of the mesh, mainly managing the set of degrees of freedom. More...

#include <fespace.hpp>

Inheritance diagram for mfem::FiniteElementSpace:

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Collaboration diagram for mfem::FiniteElementSpace:

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Classes
class	DerefinementOperator
	Derefinement operator, used by the friend class InterpolationGridTransfer. More...

struct	key_hash

class	RefinementOperator
	GridFunction interpolation operator applicable after mesh refinement. More...

Public Member Functions
	FiniteElementSpace ()
	Default constructor: the object is invalid until initialized using the method Load().

	FiniteElementSpace (const FiniteElementSpace &orig, Mesh mesh=NULL, const FiniteElementCollection fec=NULL)
	Copy constructor: deep copy all data from orig except the Mesh, the FiniteElementCollection, and some derived data.

	FiniteElementSpace (Mesh mesh, const FiniteElementCollection fec, int vdim=1, int ordering=Ordering::byNODES)

	FiniteElementSpace (Mesh mesh, NURBSExtension ext, const FiniteElementCollection *fec, int vdim=1, int ordering=Ordering::byNODES)
	Construct a NURBS FE space based on the given NURBSExtension, ext.

FiniteElementSpace &	operator= (const FiniteElementSpace &)=delete
	Copy assignment not supported.

Mesh *	GetMesh () const
	Returns the mesh.

const NURBSExtension *	GetNURBSext () const

NURBSExtension *	GetNURBSext ()

NURBSExtension *	StealNURBSext ()

bool	Conforming () const

bool	Nonconforming () const

void	SetElementOrder (int i, int p)
	Sets the order of the i'th finite element.

int	GetElementOrder (int i) const
	Returns the order of the i'th finite element.

int	GetMaxElementOrder () const
	Return the maximum polynomial order.

bool	IsVariableOrder () const
	Returns true if the space contains elements of varying polynomial orders.

const SparseMatrix *	GetConformingProlongation () const
	The returned SparseMatrix is owned by the FiniteElementSpace.

const SparseMatrix *	GetConformingRestriction () const
	The returned SparseMatrix is owned by the FiniteElementSpace.

const SparseMatrix *	GetHpConformingRestriction () const
	The returned SparseMatrix is owned by the FiniteElementSpace.

virtual const Operator *	GetProlongationMatrix () const
	The returned Operator is owned by the FiniteElementSpace.

const Operator *	GetRestrictionTransposeOperator () const
	Return an operator that performs the transpose of GetRestrictionOperator.

virtual const Operator *	GetRestrictionOperator () const
	An abstract operator that performs the same action as GetRestrictionMatrix.

virtual const SparseMatrix *	GetRestrictionMatrix () const
	The returned SparseMatrix is owned by the FiniteElementSpace.

virtual const SparseMatrix *	GetHpRestrictionMatrix () const
	The returned SparseMatrix is owned by the FiniteElementSpace.

const ElementRestrictionOperator *	GetElementRestriction (ElementDofOrdering e_ordering) const
	Return an Operator that converts L-vectors to E-vectors.

virtual const FaceRestriction *	GetFaceRestriction (ElementDofOrdering f_ordering, FaceType, L2FaceValues mul=L2FaceValues::DoubleValued) const
	Return an Operator that converts L-vectors to E-vectors on each face.

const QuadratureInterpolator *	GetQuadratureInterpolator (const IntegrationRule &ir) const
	Return a QuadratureInterpolator that interpolates E-vectors to quadrature point values and/or derivatives (Q-vectors).

const QuadratureInterpolator *	GetQuadratureInterpolator (const QuadratureSpace &qs) const
	Return a QuadratureInterpolator that interpolates E-vectors to quadrature point values and/or derivatives (Q-vectors).

const FaceQuadratureInterpolator *	GetFaceQuadratureInterpolator (const IntegrationRule &ir, FaceType type) const
	Return a FaceQuadratureInterpolator that interpolates E-vectors to quadrature point values and/or derivatives (Q-vectors).

int	GetOrder (int i) const
	Returns the polynomial degree of the i'th finite element.

int	GetEdgeOrder (int edge, int variant=0) const

int	GetFaceOrder (int face, int variant=0) const
	Returns the polynomial degree of the i'th face finite element.

int	GetVDim () const
	Returns vector dimension.

int	GetNDofs () const
	Returns number of degrees of freedom. This is the number of Local Degrees of Freedom.

int	GetVSize () const
	Return the number of vector dofs, i.e. GetNDofs() x GetVDim().

virtual int	GetTrueVSize () const
	Return the number of vector true (conforming) dofs.

int	GetNConformingDofs () const

int	GetConformingVSize () const

Ordering::Type	GetOrdering () const
	Return the ordering method.

const FiniteElementCollection *	FEColl () const

int	GetNVDofs () const
	Number of all scalar vertex dofs.

int	GetNEDofs () const
	Number of all scalar edge-interior dofs.

int	GetNFDofs () const
	Number of all scalar face-interior dofs.

int	GetNV () const
	Returns number of vertices in the mesh.

int	GetNE () const
	Returns number of elements in the mesh.

int	GetNF () const
	Returns number of faces (i.e. co-dimension 1 entities) in the mesh.

int	GetNBE () const
	Returns number of boundary elements in the mesh.

int	GetNFbyType (FaceType type) const
	Returns the number of faces according to the requested type.

int	GetElementType (int i) const
	Returns the type of element i.

void	GetElementVertices (int i, Array< int > &vertices) const
	Returns the vertices of element i.

int	GetBdrElementType (int i) const
	Returns the type of boundary element i.

ElementTransformation *	GetElementTransformation (int i) const
	Returns ElementTransformation for the i-th element.

void	GetElementTransformation (int i, IsoparametricTransformation *ElTr)
	Returns the transformation defining the i-th element in the user-defined variable ElTr.

ElementTransformation *	GetBdrElementTransformation (int i) const
	Returns ElementTransformation for the i-th boundary element.

int	GetAttribute (int i) const

int	GetBdrAttribute (int i) const

void	GetPatchDofs (int patch, Array< int > &dofs) const
	Returns indices of degrees of freedom for NURBS patch index patch. Cartesian ordering is used, for the tensor-product degrees of freedom.

MFEM_DEPRECATED void	RebuildElementToDofTable ()
	(

void	ReorderElementToDofTable ()
	Reorder the scalar DOFs based on the element ordering.

const Table *	GetElementToFaceOrientationTable () const

const Table &	GetElementToDofTable () const
	Return a reference to the internal Table that stores the lists of scalar dofs, for each mesh element, as returned by GetElementDofs().

const Table &	GetBdrElementToDofTable () const
	Return a reference to the internal Table that stores the lists of scalar dofs, for each boundary mesh element, as returned by GetBdrElementDofs().

const Table &	GetFaceToDofTable () const
	Return a reference to the internal Table that stores the lists of scalar dofs, for each face in the mesh, as returned by GetFaceDofs(). In this context, "face" refers to a (dim-1)-dimensional mesh entity.

void	BuildDofToArrays ()
	Initialize internal data that enables the use of the methods GetElementForDof() and GetLocalDofForDof().

int	GetElementForDof (int i) const
	Return the index of the first element that contains dof i.

int	GetLocalDofForDof (int i) const
	Return the local dof index in the first element that contains dof i.

virtual const FiniteElement *	GetFE (int i) const
	Returns pointer to the FiniteElement in the FiniteElementCollection associated with i'th element in the mesh object. Note: The method has been updated to abort instead of returning NULL for an empty partition.

const FiniteElement *	GetBE (int i) const
	Returns pointer to the FiniteElement in the FiniteElementCollection associated with i'th boundary face in the mesh object.

const FiniteElement *	GetFaceElement (int i) const
	Returns pointer to the FiniteElement in the FiniteElementCollection associated with i'th face in the mesh object. Faces in this case refer to the MESHDIM-1 primitive so in 2D they are segments and in 1D they are points.

const FiniteElement *	GetEdgeElement (int i, int variant=0) const
	Returns pointer to the FiniteElement in the FiniteElementCollection associated with i'th edge in the mesh object.

const FiniteElement *	GetTraceElement (int i, Geometry::Type geom_type) const
	Return the trace element from element 'i' to the given 'geom_type'.

virtual void	GetEssentialVDofs (const Array< int > &bdr_attr_is_ess, Array< int > &ess_vdofs, int component=-1) const
	Mark degrees of freedom associated with boundary elements with the specified boundary attributes (marked in 'bdr_attr_is_ess'). For spaces with 'vdim' > 1, the 'component' parameter can be used to restricts the marked vDOFs to the specified component.

virtual void	GetEssentialTrueDofs (const Array< int > &bdr_attr_is_ess, Array< int > &ess_tdof_list, int component=-1) const
	Get a list of essential true dofs, ess_tdof_list, corresponding to the boundary attributes marked in the array bdr_attr_is_ess. For spaces with 'vdim' > 1, the 'component' parameter can be used to restricts the marked tDOFs to the specified component.

void	GetBoundaryTrueDofs (Array< int > &boundary_dofs, int component=-1)
	Get a list of all boundary true dofs, boundary_dofs. For spaces with 'vdim' > 1, the 'component' parameter can be used to restricts the marked tDOFs to the specified component. Equivalent to FiniteElementSpace::GetEssentialTrueDofs with all boundary attributes marked as essential.

void	ConvertToConformingVDofs (const Array< int > &dofs, Array< int > &cdofs)
	For a partially conforming FE space, convert a marker array (nonzero entries are true) on the partially conforming dofs to a marker array on the conforming dofs. A conforming dofs is marked iff at least one of its dependent dofs is marked.

void	ConvertFromConformingVDofs (const Array< int > &cdofs, Array< int > &dofs)
	For a partially conforming FE space, convert a marker array (nonzero entries are true) on the conforming dofs to a marker array on the (partially conforming) dofs. A dof is marked iff it depends on a marked conforming dofs, where dependency is defined by the ConformingRestriction matrix; in other words, a dof is marked iff it corresponds to a marked conforming dof.

SparseMatrix *	D2C_GlobalRestrictionMatrix (FiniteElementSpace *cfes)
	Generate the global restriction matrix from a discontinuous FE space to the continuous FE space of the same polynomial degree.

SparseMatrix *	D2Const_GlobalRestrictionMatrix (FiniteElementSpace *cfes)
	Generate the global restriction matrix from a discontinuous FE space to the piecewise constant FE space.

SparseMatrix *	H2L_GlobalRestrictionMatrix (FiniteElementSpace *lfes)
	Construct the restriction matrix from the FE space given by (this) to the lower degree FE space given by (lfes) which is defined on the same mesh.

void	GetTransferOperator (const FiniteElementSpace &coarse_fes, OperatorHandle &T) const
	Construct and return an Operator that can be used to transfer GridFunction data from coarse_fes, defined on a coarse mesh, to this FE space, defined on a refined mesh.

virtual void	GetTrueTransferOperator (const FiniteElementSpace &coarse_fes, OperatorHandle &T) const
	Construct and return an Operator that can be used to transfer true-dof data from coarse_fes, defined on a coarse mesh, to this FE space, defined on a refined mesh.

virtual void	Update (bool want_transform=true)
	Reflect changes in the mesh: update number of DOFs, etc. Also, calculate GridFunction transformation operator (unless want_transform is false). Safe to call multiple times, does nothing if space already up to date.

const Operator *	GetUpdateOperator ()
	Get the GridFunction update operator.

void	GetUpdateOperator (OperatorHandle &T)
	Return the update operator in the given OperatorHandle, T.

void	SetUpdateOperatorOwner (bool own)
	Set the ownership of the update operator: if set to false, the Operator returned by GetUpdateOperator() must be deleted outside the FiniteElementSpace.

void	SetUpdateOperatorType (Operator::Type tid)
	Specify the Operator::Type to be used by the update operators.

virtual void	UpdatesFinished ()
	Free the GridFunction update operator (if any), to save memory.

long	GetSequence () const

bool	IsDGSpace () const
	Return whether or not the space is discontinuous (L2)

void	SetRelaxedHpConformity (bool relaxed=true)

void	Save (std::ostream &out) const
	Save finite element space to output stream out.

FiniteElementCollection *	Load (Mesh *m, std::istream &input)
	Read a FiniteElementSpace from a stream. The returned FiniteElementCollection is owned by the caller.

virtual	~FiniteElementSpace ()

Local DoF Access Members
These member functions produce arrays of local degree of freedom indices, see ldof. If vdim == 1 these indices can be used to access entries in GridFunction, LinearForm, and BilinearForm objects. If vdim != 1 the corresponding Get*VDofs methods should be used instead or one of the DofToVDof methods could be used to produce the appropriate offsets from these local dofs.
DofTransformation *	GetElementDofs (int elem, Array< int > &dofs) const
	Returns indices of degrees of freedom of element 'elem'. The returned indices are offsets into an ldof vector. See also GetElementVDofs().

virtual void	GetElementDofs (int elem, Array< int > &dofs, DofTransformation &doftrans) const
	The same as GetElementDofs(), but with a user-allocated DofTransformation object. doftrans must be allocated in advance and will be owned by the caller. The user can use the DofTransformation::GetDofTransformation method on the returned doftrans object to detect if the DofTransformation should actually be used.

DofTransformation *	GetBdrElementDofs (int bel, Array< int > &dofs) const
	Returns indices of degrees of freedom for boundary element 'bel'. The returned indices are offsets into an ldof vector. See also GetBdrElementVDofs().

virtual void	GetBdrElementDofs (int bel, Array< int > &dofs, DofTransformation &doftrans) const
	The same as GetBdrElementDofs(), but with a user-allocated DofTransformation object. doftrans must be allocated in advance and will be owned by the caller. The user can use the DofTransformation::GetDofTransformation method on the returned doftrans object to detect if the DofTransformation should actually be used.

virtual int	GetFaceDofs (int face, Array< int > &dofs, int variant=0) const
	Returns the indices of the degrees of freedom for the specified face, including the DOFs for the edges and the vertices of the face.

int	GetEdgeDofs (int edge, Array< int > &dofs, int variant=0) const
	Returns the indices of the degrees of freedom for the specified edge, including the DOFs for the vertices of the edge.

void	GetVertexDofs (int i, Array< int > &dofs) const
	Returns the indices of the degrees of freedom for the specified vertices.

void	GetElementInteriorDofs (int i, Array< int > &dofs) const
	Returns the indices of the degrees of freedom for the interior of the specified element.

int	GetNumElementInteriorDofs (int i) const
	Returns the number of degrees of freedom associated with the interior of the specified element.

void	GetFaceInteriorDofs (int i, Array< int > &dofs) const
	Returns the indices of the degrees of freedom for the interior of the specified face.

void	GetEdgeInteriorDofs (int i, Array< int > &dofs) const
	Returns the indices of the degrees of freedom for the interior of the specified edge.

DoF To VDoF Conversion methods
These methods convert between local dof and local vector dof using the appropriate relationship based on the Ordering::Type defined in this FiniteElementSpace object. These methods assume the index set has a range [0, GetNDofs()) which will be mapped to the range [0, GetVSize()). This assumption can be changed in the forward mappings by passing a value for ndofs which differs from that returned by GetNDofs(). Note These methods, with the exception of VDofToDof(), are designed to produce the correctly encoded values when dof entries are negative, see ldof for more on negative dof indices. Warning When MFEM_DEBUG is enabled at build time the forward mappings will verify that each dof lies in the proper range. If MFEM_DEBUG is disabled no range checking is performed.
void	GetVDofs (int vd, Array< int > &dofs, int ndofs=-1) const
	Returns the indices of all of the VDofs for the specified dimension 'vd'.

void	DofsToVDofs (Array< int > &dofs, int ndofs=-1) const
	Compute the full set of vdofs corresponding to each entry in dofs.

void	DofsToVDofs (int vd, Array< int > &dofs, int ndofs=-1) const
	Compute the set of vdofs corresponding to each entry in dofs for the given vector index vd.

int	DofToVDof (int dof, int vd, int ndofs=-1) const
	Compute a single vdof corresponding to the index dof and the vector index vd.

int	VDofToDof (int vdof) const
	Compute the inverse of the Dof to VDof mapping for a single index vdof.

Local Vector DoF Access Members
These member functions produce arrays of local vector degree of freedom indices, see ldof and vdof. These indices can be used to access entries in GridFunction, LinearForm, and BilinearForm objects regardless of the value of vdim.
DofTransformation *	GetElementVDofs (int i, Array< int > &vdofs) const
	Returns indices of degrees of freedom for the i'th element. The returned indices are offsets into an ldof vector with vdim not necessarily equal to 1. The returned indices are always ordered byNODES, irrespective of whether the space is byNODES or byVDIM. See also GetElementDofs().

void	GetElementVDofs (int i, Array< int > &vdofs, DofTransformation &doftrans) const
	The same as GetElementVDofs(), but with a user-allocated DofTransformation object. doftrans must be allocated in advance and will be owned by the caller. The user can use the DofTransformation::GetDofTransformation method on the returned doftrans object to detect if the DofTransformation should actually be used.

DofTransformation *	GetBdrElementVDofs (int i, Array< int > &vdofs) const
	Returns indices of degrees of freedom for i'th boundary element. The returned indices are offsets into an ldof vector with vdim not necessarily equal to 1. See also GetBdrElementDofs().

void	GetBdrElementVDofs (int i, Array< int > &vdofs, DofTransformation &doftrans) const
	The same as GetBdrElementVDofs(), but with a user-allocated DofTransformation object. doftrans must be allocated in advance and will be owned by the caller. The user can use the DofTransformation::GetDofTransformation method on the returned doftrans object to detect if the DofTransformation should actually be used.

void	GetPatchVDofs (int i, Array< int > &vdofs) const
	Returns indices of degrees of freedom in vdofs for NURBS patch i.

void	GetFaceVDofs (int i, Array< int > &vdofs) const
	Returns the indices of the degrees of freedom for the specified face, including the DOFs for the edges and the vertices of the face.

void	GetEdgeVDofs (int i, Array< int > &vdofs) const
	Returns the indices of the degrees of freedom for the specified edge, including the DOFs for the vertices of the edge.

void	GetVertexVDofs (int i, Array< int > &vdofs) const
	Returns the indices of the degrees of freedom for the specified vertices.

void	GetElementInteriorVDofs (int i, Array< int > &vdofs) const
	Returns the indices of the degrees of freedom for the interior of the specified element.

void	GetEdgeInteriorVDofs (int i, Array< int > &vdofs) const
	Returns the indices of the degrees of freedom for the interior of the specified edge.

Static Public Member Functions
static void	AdjustVDofs (Array< int > &vdofs)
	Remove the orientation information encoded into an array of dofs Some basis function types have a relative orientation associated with degrees of freedom shared between neighboring elements, see ldof for more information. An orientation mismatch is indicated in the dof indices by a negative index value. This method replaces such negative indices with the corresponding positive offsets.

static int	EncodeDof (int entity_base, int idx)
	Helper to encode a sign flip into a DOF index (for Hcurl/Hdiv shapes).

static int	DecodeDof (int dof)
	Helper to return the DOF associated with a sign encoded DOF.

static int	DecodeDof (int dof, real_t &sign)
	Helper to determine the DOF and sign of a sign encoded DOF.

static void	MarkerToList (const Array< int > &marker, Array< int > &list)
	Convert a Boolean marker array to a list containing all marked indices.

static void	ListToMarker (const Array< int > &list, int marker_size, Array< int > &marker, int mark_val=-1)
	Convert an array of indices (list) to a Boolean marker array where all indices in the list are marked with the given value and the rest are set to zero.

Protected Types
using	key_face = std::tuple<bool, ElementDofOrdering, FaceType, L2FaceValues>
	The face restriction operators, see GetFaceRestriction().

using	map_L2F = std::unordered_map<const key_face,FaceRestriction*,key_hash>

typedef std::uint64_t	VarOrderBits
	Bit-mask representing a set of orders needed by an edge/face.

Protected Member Functions
void	UpdateNURBS ()

void	Construct ()

void	Destroy ()

void	ConstructDoFTransArray ()

void	DestroyDoFTransArray ()

void	BuildElementToDofTable () const

void	BuildBdrElementToDofTable () const

void	BuildFaceToDofTable () const

void	BuildNURBSFaceToDofTable () const
	Generates partial face_dof table for a NURBS space.

int	GetElementOrderImpl (int i) const
	Return element order: internal version of GetElementOrder without checks.

void	CalcEdgeFaceVarOrders (Array< VarOrderBits > &edge_orders, Array< VarOrderBits > &face_orders) const

int	MakeDofTable (int ent_dim, const Array< int > &entity_orders, Table &entity_dofs, Array< char > *var_ent_order)

int	FindDofs (const Table &var_dof_table, int row, int ndof) const
	Search row of a DOF table for a DOF set of size 'ndof', return first DOF.

int	FindEdgeDof (int edge, int ndof) const

int	FindFaceDof (int face, int ndof) const
	Similar to FindEdgeDof, but used for mixed meshes too.

int	FirstFaceDof (int face, int variant=0) const

int	GetNVariants (int entity, int index) const
	Return number of possible DOF variants for edge/face (var. order spaces).

int	GetEntityDofs (int entity, int index, Array< int > &dofs, Geometry::Type master_geom=Geometry::INVALID, int variant=0) const
	Helper to get vertex, edge or face DOFs (entity=0,1,2 resp.).

int	GetEntityVDofs (int entity, int index, Array< int > &dofs, Geometry::Type master_geom=Geometry::INVALID, int variant=0) const
	Helper to get vertex, edge or face VDOFs (entity=0,1,2 resp.).

int	GetDegenerateFaceDofs (int index, Array< int > &dofs, Geometry::Type master_geom, int variant) const

int	GetNumBorderDofs (Geometry::Type geom, int order) const

void	BuildConformingInterpolation () const
	Calculate the cP and cR matrices for a nonconforming mesh.

void	AddEdgeFaceDependencies (SparseMatrix &deps, Array< int > &master_dofs, const FiniteElement master_fe, Array< int > &slave_dofs, int slave_face, const DenseMatrix pm) const

void	MakeVDimMatrix (SparseMatrix &mat) const
	Replicate 'mat' in the vector dimension, according to vdim ordering mode.

SparseMatrix *	RefinementMatrix_main (const int coarse_ndofs, const Table &coarse_elem_dof, const Table *coarse_elem_fos, const DenseTensor localP[]) const

void	GetLocalRefinementMatrices (Geometry::Type geom, DenseTensor &localP) const

void	GetLocalDerefinementMatrices (Geometry::Type geom, DenseTensor &localR) const

SparseMatrix *	RefinementMatrix (int old_ndofs, const Table old_elem_dof, const Table old_elem_fos)

SparseMatrix *	DerefinementMatrix (int old_ndofs, const Table old_elem_dof, const Table old_elem_fos)
	Calculate GridFunction restriction matrix after mesh derefinement.

void	GetLocalRefinementMatrices (const FiniteElementSpace &coarse_fes, Geometry::Type geom, DenseTensor &localP) const
	Return in localP the local refinement matrices that map between fespaces after mesh refinement.

void	Constructor (Mesh mesh, NURBSExtension ext, const FiniteElementCollection *fec, int vdim=1, int ordering=Ordering::byNODES)
	Help function for constructors + Load().

virtual void	UpdateMeshPointer (Mesh *new_mesh)

void	UpdateElementOrders ()
	Resize the elem_order array on mesh change.

virtual void	CopyProlongationAndRestriction (const FiniteElementSpace &fes, const Array< int > *perm)
	Copies the prolongation and restriction matrices from fes.

Static Protected Member Functions
static int	MinOrder (VarOrderBits bits)
	Return the minimum order (least significant bit set) in the bit mask.

static void	AddDependencies (SparseMatrix &deps, Array< int > &master_dofs, Array< int > &slave_dofs, DenseMatrix &I, int skipfirst=0)

static bool	DofFinalizable (int dof, const Array< bool > &finalized, const SparseMatrix &deps)

Protected Attributes
Mesh *	mesh
	The mesh that FE space lives on (not owned).

const FiniteElementCollection *	fec
	Associated FE collection (not owned).

int	vdim
	Vector dimension (number of unknowns per degree of freedom).

Ordering::Type	ordering

int	ndofs
	Number of degrees of freedom. Number of unknowns is ndofs * vdim.

Array< char >	elem_order

int	nvdofs

int	nedofs

int	nfdofs

int	nbdofs

int	uni_fdof

int *	bdofs
	internal DOFs of elements if mixed/var-order; NULL otherwise

Table	var_edge_dofs

Table	var_face_dofs
	NOTE: also used for spaces with mixed faces.

Array< char >	var_edge_orders

Array< char >	var_face_orders

Table *	elem_dof

Table *	elem_fos

Table *	bdr_elem_dof

Table *	bdr_elem_fos

Table *	face_dof

Array< int >	dof_elem_array

Array< int >	dof_ldof_array

NURBSExtension *	NURBSext

int	own_ext

Array< int >	face_to_be

Array< StatelessDofTransformation * >	DoFTransArray

DofTransformation	DoFTrans

std::unique_ptr< SparseMatrix >	cP

std::unique_ptr< SparseMatrix >	cR
	Conforming restriction matrix such that cR.cP=I.

std::unique_ptr< SparseMatrix >	cR_hp
	A version of the conforming restriction matrix for variable-order spaces.

bool	cP_is_set

std::unique_ptr< Operator >	R_transpose
	Operator computing the action of the transpose of the restriction.

OperatorHandle	Th
	Transformation to apply to GridFunctions after space Update().

OperatorHandle	L2E_nat
	The element restriction operators, see GetElementRestriction().

OperatorHandle	L2E_lex

map_L2F	L2F

Array< QuadratureInterpolator * >	E2Q_array

Array< FaceQuadratureInterpolator * >	E2IFQ_array

Array< FaceQuadratureInterpolator * >	E2BFQ_array

long	sequence

long	mesh_sequence

bool	orders_changed
	True if at least one element order changed (variable-order space only).

bool	relaxed_hp

Static Protected Attributes
static constexpr int	MaxVarOrder = 8*sizeof(VarOrderBits) - 1

Friends
class	InterpolationGridTransfer

class	PRefinementTransferOperator

class	LORBase

void	Mesh::Swap (Mesh &, bool)

Detailed Description

Class FiniteElementSpace - responsible for providing FEM view of the mesh, mainly managing the set of degrees of freedom.

The term "degree of freedom", or "dof" for short, can mean different things in different contexts. In MFEM we use "dof" to refer to four closely related types of data; edofs, ldofs, tdofs, and vdofs.

Element DoF:: Element dofs, sometimes referred to as edofs, are the expansion coefficients used to build the linear combination of basis functions which approximate a field within one element of the computational mesh. The arrangement of the element dofs is determined by the basis function and element types.

: Element dofs are usually accessed one element at a time but they can be concatenated together into a global vector when minimizing access time is crucial. The global number of element dofs is not directly available from the FiniteElementSpace. It can be determined by repeatedly calling FiniteElementSpace::GetElementDofs and summing the lengths of the resulting dofs arrays.

Local DoF:: Most basis function types share many of their element dofs with neighboring elements. Consequently, the global edof vector suggested above would contain many redundant entries. One of the primary roles of the FiniteElementSpace is to collapse out these redundancies and define a unique ordering of the remaining degrees of freedom. The collapsed set of dofs are called "local dofs" or ldofs in the MFEM parlance.

: The term local in this context refers to the local rank in a parallel processing environment. MFEM can, of course, be used in sequential computing environments but it is designed with parallel processing in mind and this terminology reflects that design focus.

: When running in parallel the set of local dofs contains all of the degrees of freedom associated with locally owned elements. When running in serial all elements are locally owned so all element dofs are represented in the set of local dofs.

: There are two important caveats regarding local dofs. First, some basis function types, Nedelec and Raviart-Thomas are the prime examples, have an orientation associated with each basis function. The relative orientations of such basis functions in neighboring elements can lead to shared degrees of freedom with opposite signs from the point of view of these neighboring elements. MFEM typically chooses the orientation of the first such shared degree of freedom that it encounters as the default orientation for the corresponding local dof. When this local dof is referenced by a neighboring element which happens to require the opposite orientation the local dof index will be returned (by calls to functions such as FiniteElementSpace::GetElementDofs) as a negative integer. In such cases the actual offset into the vector of local dofs is -index-1 and the value expected by this element should have the opposite sign to the value stored in the local dof vector.

: The second important caveat only pertains to high order Nedelec basis functions when shared triangular faces are present in the mesh. In this very particular case the relative orientation of the face with respect to its two neighboring elements can lead to different definitions of the degrees of freedom associated with the interior of the face which cannot be handled by simply flipping the signs of the corresponding values. The DofTransformation class is designed to manage the necessary edof to ldof transformations in this case. In the majority of cases the DofTransformation is unnecessary and a NULL pointer will be returned in place of a pointer to this object. See DofTransformation for more information.

True DoF:: As the name suggests "true dofs" or tdofs form the minimal set of data values needed (along with mesh and basis function definitions) to uniquely define a finite element discretization of a field. The number of true dofs determines the size of the linear systems which typically need to be solved in FEM simulations.

: Often the true dofs and the local dofs are identical, however, there are important cases where they differ significantly. The first such case is related to non-conforming meshes. On non-conforming meshes it is common for degrees of freedom associated with "hanging" nodes, edges, or faces to be constrained by degrees of freedom associated with another mesh entity. In such cases the "hanging" degrees of freedom should not be considered "true" degrees of freedom since their values cannot be independently assigned. For this reason the FiniteElementSpace must process these constraints and define a reduced set of "true" degrees of freedom which are distinct from the local degrees of freedom.

: The second important distinction arises in parallel processing. When distributing a linear system in parallel each degree of freedom must be assigned to a particular processor, its owner. From the finite element point of view it is convenient to distribute a computational mesh and define an owning processor for each element. Since degrees of freedom may be shared between neighboring elements they may also be shared between neighboring processors. Another role of the FiniteElementSpace is to identify the ownership of degrees of freedom which must be shared between processors. Therefore the set of "true" degrees of freedom must also remove redundant degrees of freedom which are owned by other processors.

: To summarize the set of true degrees of freedom are those degrees of freedom needed to solve a linear system representing the partial differential equation being modeled. True dofs differ from "local" dofs by eliminating redundancies across processor boundaries and applying the constraints needed to properly define fields on non-conforming meshes.

Vector DoF:: Vector dofs or vdofs are related to fields which are constructed using multiple copies of the same set of basis functions. A typical example would be the use of three instances of the scalar H1 basis functions to approximate the x, y, and z components of a displacement vector field in three dimensional space as often seen in elasticity simulations.

: Vector dofs do not represent a specific index space the way the three previous types of dofs do. Rather they are related to modifications of these other index spaces to accomodate multiple copies of the underlying function spaces.

: When using vdofs, i.e. when vdim != 1, the FiniteElementSpace only manages a single set of degrees of freedom and then uses simple rules to determine the appropriate offsets into the full index spaces. Two ordering rules are supported; byNODES and byVDIM. See Ordering::Type for details.

: Clearly the notion of a vdof is relevant in each of the three contexts mentioned above so extra care must be taken whenever vdim != 1 to ensure that the edof, ldof, or tdof is being interpreted correctly.

Definition at line 219 of file fespace.hpp.

Member Typedef Documentation

◆ key_face

using mfem::FiniteElementSpace::key_face = std::tuple<bool, ElementDofOrdering, FaceType, L2FaceValues>

protected

The face restriction operators, see GetFaceRestriction().

Definition at line 295 of file fespace.hpp.

◆ map_L2F

using mfem::FiniteElementSpace::map_L2F = std::unordered_map<const key_face,FaceRestriction*,key_hash>

protected

Definition at line 306 of file fespace.hpp.

◆ VarOrderBits

typedef std::uint64_t mfem::FiniteElementSpace::VarOrderBits

protected

Bit-mask representing a set of orders needed by an edge/face.

Definition at line 345 of file fespace.hpp.

Constructor & Destructor Documentation

◆ FiniteElementSpace() [1/4]

mfem::FiniteElementSpace::FiniteElementSpace ( )

Default constructor: the object is invalid until initialized using the method Load().

Definition at line 59 of file fespace.cpp.

◆ FiniteElementSpace() [2/4]

mfem::FiniteElementSpace::FiniteElementSpace	(	const FiniteElementSpace &	orig,
		Mesh *	mesh = NULL,
		const FiniteElementCollection *	fec = NULL )

Copy constructor: deep copy all data from orig except the Mesh, the FiniteElementCollection, and some derived data.

If the mesh or fec pointers are NULL (default), then the new FiniteElementSpace will reuse the respective pointers from orig. If any of these pointers is not NULL, the given pointer will be used instead of the one used by orig.

Note: The objects pointed to by the mesh and fec parameters must be either the same objects as the ones used by orig, or copies of them. Otherwise, the behavior is undefined.; Derived data objects, such as the conforming prolongation and restriction matrices, and the update operator, will not be copied, even if they are created in the orig object.

Definition at line 71 of file fespace.cpp.

◆ FiniteElementSpace() [3/4]

mfem::FiniteElementSpace::FiniteElementSpace	(	Mesh *	mesh,
		const FiniteElementCollection *	fec,
		int	vdim = 1,
		int	ordering = Ordering::byNODES )

inline

Definition at line 541 of file fespace.hpp.

◆ FiniteElementSpace() [4/4]

mfem::FiniteElementSpace::FiniteElementSpace	(	Mesh *	mesh,
		NURBSExtension *	ext,
		const FiniteElementCollection *	fec,
		int	vdim = 1,
		int	ordering = Ordering::byNODES )

inline

Construct a NURBS FE space based on the given NURBSExtension, ext.

Note: If the pointer ext is NULL, this constructor is equivalent to the standard constructor with the same arguments minus the NURBSExtension, ext.

Definition at line 550 of file fespace.hpp.

◆ ~FiniteElementSpace()

mfem::FiniteElementSpace::~FiniteElementSpace ( )

virtual

Definition at line 3282 of file fespace.cpp.

Member Function Documentation

◆ AddDependencies()

void mfem::FiniteElementSpace::AddDependencies	(	SparseMatrix &	deps,
		Array< int > &	master_dofs,
		Array< int > &	slave_dofs,
		DenseMatrix &	I,
		int	skipfirst = 0 )

staticprotected

Definition at line 807 of file fespace.cpp.

◆ AddEdgeFaceDependencies()

void mfem::FiniteElementSpace::AddEdgeFaceDependencies	(	SparseMatrix &	deps,
		Array< int > &	master_dofs,
		const FiniteElement *	master_fe,
		Array< int > &	slave_dofs,
		int	slave_face,
		const DenseMatrix *	pm ) const

protected

Definition at line 832 of file fespace.cpp.

◆ AdjustVDofs()

void mfem::FiniteElementSpace::AdjustVDofs ( Array< int > & vdofs )

static

Remove the orientation information encoded into an array of dofs Some basis function types have a relative orientation associated with degrees of freedom shared between neighboring elements, see ldof for more information. An orientation mismatch is indicated in the dof indices by a negative index value. This method replaces such negative indices with the corresponding positive offsets.

Note: The name of this method reflects the fact that it is most often applied to sets of Vector Dofs but it would work equally well on sets of Local Dofs.

Definition at line 265 of file fespace.cpp.

◆ BuildBdrElementToDofTable()

void mfem::FiniteElementSpace::BuildBdrElementToDofTable ( ) const

protected

Definition at line 387 of file fespace.cpp.

◆ BuildConformingInterpolation()

void mfem::FiniteElementSpace::BuildConformingInterpolation ( ) const

protected

Calculate the cP and cR matrices for a nonconforming mesh.

Definition at line 985 of file fespace.cpp.

◆ BuildDofToArrays()

void mfem::FiniteElementSpace::BuildDofToArrays ( )

Initialize internal data that enables the use of the methods GetElementForDof() and GetLocalDofForDof().

Definition at line 481 of file fespace.cpp.

◆ BuildElementToDofTable()

void mfem::FiniteElementSpace::BuildElementToDofTable ( ) const

protected

Definition at line 346 of file fespace.cpp.

◆ BuildFaceToDofTable()

void mfem::FiniteElementSpace::BuildFaceToDofTable ( ) const

protected

Definition at line 426 of file fespace.cpp.

◆ BuildNURBSFaceToDofTable()

void mfem::FiniteElementSpace::BuildNURBSFaceToDofTable ( ) const

protected

Generates partial face_dof table for a NURBS space.

The table is only defined for exterior faces that coincide with a boundary.

Definition at line 2325 of file fespace.cpp.

◆ CalcEdgeFaceVarOrders()

void mfem::FiniteElementSpace::CalcEdgeFaceVarOrders	(	Array< VarOrderBits > &	edge_orders,
		Array< VarOrderBits > &	face_orders ) const

protected

In a variable order space, calculate a bitmask of polynomial orders that need to be represented on each edge and face.

Definition at line 2513 of file fespace.cpp.

◆ Conforming()

bool mfem::FiniteElementSpace::Conforming ( ) const

inline

Definition at line 565 of file fespace.hpp.

◆ Construct()

void mfem::FiniteElementSpace::Construct ( )

protected

Definition at line 2374 of file fespace.cpp.

◆ ConstructDoFTransArray()

void mfem::FiniteElementSpace::ConstructDoFTransArray ( )

protected

Definition at line 2252 of file fespace.cpp.

◆ Constructor()

void mfem::FiniteElementSpace::Constructor	(	Mesh *	mesh,
		NURBSExtension *	ext,
		const FiniteElementCollection *	fec,
		int	vdim = 1,
		int	ordering = Ordering::byNODES )

protected

Help function for constructors + Load().

Definition at line 2198 of file fespace.cpp.

◆ ConvertFromConformingVDofs()

void mfem::FiniteElementSpace::ConvertFromConformingVDofs	(	const Array< int > &	cdofs,
		Array< int > &	dofs )

For a partially conforming FE space, convert a marker array (nonzero entries are true) on the conforming dofs to a marker array on the (partially conforming) dofs. A dof is marked iff it depends on a marked conforming dofs, where dependency is defined by the ConformingRestriction matrix; in other words, a dof is marked iff it corresponds to a marked conforming dof.

Definition at line 688 of file fespace.cpp.

◆ ConvertToConformingVDofs()

void mfem::FiniteElementSpace::ConvertToConformingVDofs	(	const Array< int > &	dofs,
		Array< int > &	cdofs )

For a partially conforming FE space, convert a marker array (nonzero entries are true) on the partially conforming dofs to a marker array on the conforming dofs. A conforming dofs is marked iff at least one of its dependent dofs is marked.

Definition at line 680 of file fespace.cpp.

◆ CopyProlongationAndRestriction()

void mfem::FiniteElementSpace::CopyProlongationAndRestriction	(	const FiniteElementSpace &	fes,
		const Array< int > *	perm )

protectedvirtual

Copies the prolongation and restriction matrices from fes.

Used for low order preconditioning on non-conforming meshes. If the DOFs require a permutation, it will be supplied by non-NULL perm. NULL perm indicates that no permutation is required.

Definition at line 98 of file fespace.cpp.

◆ D2C_GlobalRestrictionMatrix()

SparseMatrix * mfem::FiniteElementSpace::D2C_GlobalRestrictionMatrix ( FiniteElementSpace * cfes )

Generate the global restriction matrix from a discontinuous FE space to the continuous FE space of the same polynomial degree.

Definition at line 697 of file fespace.cpp.

◆ D2Const_GlobalRestrictionMatrix()

SparseMatrix * mfem::FiniteElementSpace::D2Const_GlobalRestrictionMatrix ( FiniteElementSpace * cfes )

Generate the global restriction matrix from a discontinuous FE space to the piecewise constant FE space.

Definition at line 729 of file fespace.cpp.

◆ DecodeDof() [1/2]

static int mfem::FiniteElementSpace::DecodeDof ( int dof )

inlinestatic

Helper to return the DOF associated with a sign encoded DOF.

Definition at line 1017 of file fespace.hpp.

◆ DecodeDof() [2/2]

static int mfem::FiniteElementSpace::DecodeDof	(	int	dof,
		real_t &	sign )

inlinestatic

Helper to determine the DOF and sign of a sign encoded DOF.

Definition at line 1021 of file fespace.hpp.

◆ DerefinementMatrix()

SparseMatrix * mfem::FiniteElementSpace::DerefinementMatrix	(	int	old_ndofs,
		const Table *	old_elem_dof,
		const Table *	old_elem_fos )

protected

Calculate GridFunction restriction matrix after mesh derefinement.

TODO: Implement DofTransformation support

Definition at line 2095 of file fespace.cpp.

◆ Destroy()

void mfem::FiniteElementSpace::Destroy ( )

protected

Definition at line 3287 of file fespace.cpp.

◆ DestroyDoFTransArray()

void mfem::FiniteElementSpace::DestroyDoFTransArray ( )

protected

Definition at line 3340 of file fespace.cpp.

◆ DofFinalizable()

bool mfem::FiniteElementSpace::DofFinalizable	(	int	dof,
		const Array< bool > &	finalized,
		const SparseMatrix &	deps )

staticprotected

Definition at line 886 of file fespace.cpp.

◆ DofsToVDofs() [1/2]

void mfem::FiniteElementSpace::DofsToVDofs	(	Array< int > &	dofs,
		int	ndofs = -1 ) const

Compute the full set of vdofs corresponding to each entry in dofs.

Produces a set of vdofs of length vdim * dofs.Size() corresponding to the entries contained in the dofs array.

The ndofs parameter can be used to indicate the total number of Dofs associated with each component of vdim. If ndofs is -1 (the default value), then the number of Dofs is <determined by the FiniteElementSpace::GetNDofs().

Note: The dofs array is overwritten and resized to accomodate the new values.

Definition at line 213 of file fespace.cpp.

◆ DofsToVDofs() [2/2]

void mfem::FiniteElementSpace::DofsToVDofs	(	int	vd,
		Array< int > &	dofs,
		int	ndofs = -1 ) const

Compute the set of vdofs corresponding to each entry in dofs for the given vector index vd.

The ndofs parameter can be used to indicate the total number of Dofs associated with each component of vdim. If ndofs is -1 (the default value), then the number of Dofs is <determined by the FiniteElementSpace::GetNDofs().

Note: The dofs array is overwritten with the new values but its size will not be altered.

Definition at line 228 of file fespace.cpp.

◆ DofToVDof()

int mfem::FiniteElementSpace::DofToVDof	(	int	dof,
		int	vd,
		int	ndofs = -1 ) const

Compute a single vdof corresponding to the index dof and the vector index vd.

The ndofs parameter can be used to indicate the total number of Dofs associated with each component of vdim. If ndofs is -1 (the default value), then the number of Dofs is <determined by the FiniteElementSpace::GetNDofs().

Definition at line 249 of file fespace.cpp.

◆ EncodeDof()

static int mfem::FiniteElementSpace::EncodeDof	(	int	entity_base,
		int	idx )

inlinestatic

Helper to encode a sign flip into a DOF index (for Hcurl/Hdiv shapes).

Definition at line 1013 of file fespace.hpp.

◆ FEColl()

const FiniteElementCollection * mfem::FiniteElementSpace::FEColl ( ) const

inline

Definition at line 727 of file fespace.hpp.

◆ FindDofs()

int mfem::FiniteElementSpace::FindDofs	(	const Table &	var_dof_table,
		int	row,
		int	ndof ) const

protected

Search row of a DOF table for a DOF set of size 'ndof', return first DOF.

Definition at line 2682 of file fespace.cpp.

◆ FindEdgeDof()

int mfem::FiniteElementSpace::FindEdgeDof	(	int	edge,
		int	ndof ) const

inlineprotected

In a variable order space, return edge DOFs associated with a polynomial order that has 'ndof' degrees of freedom.

Definition at line 369 of file fespace.hpp.

◆ FindFaceDof()

int mfem::FiniteElementSpace::FindFaceDof	(	int	face,
		int	ndof ) const

inlineprotected

Similar to FindEdgeDof, but used for mixed meshes too.

Definition at line 373 of file fespace.hpp.

◆ FirstFaceDof()

int mfem::FiniteElementSpace::FirstFaceDof	(	int	face,
		int	variant = 0 ) const

inlineprotected

Definition at line 376 of file fespace.hpp.

◆ GetAttribute()

int mfem::FiniteElementSpace::GetAttribute ( int i ) const

inline

Definition at line 785 of file fespace.hpp.

◆ GetBdrAttribute()

int mfem::FiniteElementSpace::GetBdrAttribute ( int i ) const

inline

Definition at line 787 of file fespace.hpp.

◆ GetBdrElementDofs() [1/2]

DofTransformation * mfem::FiniteElementSpace::GetBdrElementDofs	(	int	bel,
		Array< int > &	dofs ) const

Returns indices of degrees of freedom for boundary element 'bel'. The returned indices are offsets into an ldof vector. See also GetBdrElementVDofs().

Note: In many cases the returned DofTransformation object will be NULL. In other cases see the documentation of the DofTransformation class for guidance on its role in performing edof to ldof transformations on local vectors and matrices. At present the DofTransformation is only needed for Nedelec basis functions of order 2 and above on 3D elements with triangular faces.; The returned object should NOT be deleted by the caller.

Definition at line 2950 of file fespace.cpp.

◆ GetBdrElementDofs() [2/2]

void mfem::FiniteElementSpace::GetBdrElementDofs	(	int	bel,
		Array< int > &	dofs,
		DofTransformation &	doftrans ) const

virtual

The same as GetBdrElementDofs(), but with a user-allocated DofTransformation object. doftrans must be allocated in advance and will be owned by the caller. The user can use the DofTransformation::GetDofTransformation method on the returned doftrans object to detect if the DofTransformation should actually be used.

Reimplemented in mfem::ParFiniteElementSpace.

Definition at line 2854 of file fespace.cpp.

◆ GetBdrElementToDofTable()

const Table & mfem::FiniteElementSpace::GetBdrElementToDofTable ( ) const

inline

Return a reference to the internal Table that stores the lists of scalar dofs, for each boundary mesh element, as returned by GetBdrElementDofs().

Definition at line 1141 of file fespace.hpp.

◆ GetBdrElementTransformation()

ElementTransformation * mfem::FiniteElementSpace::GetBdrElementTransformation ( int i ) const

inline

Returns ElementTransformation for the i-th boundary element.

Definition at line 782 of file fespace.hpp.

◆ GetBdrElementType()

int mfem::FiniteElementSpace::GetBdrElementType ( int i ) const

inline

Returns the type of boundary element i.

Definition at line 769 of file fespace.hpp.

◆ GetBdrElementVDofs() [1/2]

DofTransformation * mfem::FiniteElementSpace::GetBdrElementVDofs	(	int	i,
		Array< int > &	vdofs ) const

Returns indices of degrees of freedom for i'th boundary element. The returned indices are offsets into an ldof vector with vdim not necessarily equal to 1. See also GetBdrElementDofs().

Note: In many cases the returned DofTransformation object will be NULL. In other cases see the documentation of the DofTransformation class for guidance on its role in performing edof to ldof transformations on local vectors and matrices. At present the DofTransformation is only needed for Nedelec basis functions of order 2 and above on 3D elements with triangular faces.; The returned object should NOT be deleted by the caller.

Definition at line 303 of file fespace.cpp.

◆ GetBdrElementVDofs() [2/2]

void mfem::FiniteElementSpace::GetBdrElementVDofs	(	int	i,
		Array< int > &	vdofs,
		DofTransformation &	doftrans ) const

The same as GetBdrElementVDofs(), but with a user-allocated DofTransformation object. doftrans must be allocated in advance and will be owned by the caller. The user can use the DofTransformation::GetDofTransformation method on the returned doftrans object to detect if the DofTransformation should actually be used.

Definition at line 294 of file fespace.cpp.

◆ GetBE()

const FiniteElement * mfem::FiniteElementSpace::GetBE ( int i ) const

Returns pointer to the FiniteElement in the FiniteElementCollection associated with i'th boundary face in the mesh object.

Definition at line 3204 of file fespace.cpp.

◆ GetBoundaryTrueDofs()

void mfem::FiniteElementSpace::GetBoundaryTrueDofs	(	Array< int > &	boundary_dofs,
		int	component = -1 )

Get a list of all boundary true dofs, boundary_dofs. For spaces with 'vdim' > 1, the 'component' parameter can be used to restricts the marked tDOFs to the specified component. Equivalent to FiniteElementSpace::GetEssentialTrueDofs with all boundary attributes marked as essential.

Definition at line 632 of file fespace.cpp.

◆ GetConformingProlongation()

const SparseMatrix * mfem::FiniteElementSpace::GetConformingProlongation ( ) const

The returned SparseMatrix is owned by the FiniteElementSpace.

Definition at line 1302 of file fespace.cpp.

◆ GetConformingRestriction()

const SparseMatrix * mfem::FiniteElementSpace::GetConformingRestriction ( ) const

The returned SparseMatrix is owned by the FiniteElementSpace.

Definition at line 1309 of file fespace.cpp.

◆ GetConformingVSize()

int mfem::FiniteElementSpace::GetConformingVSize ( ) const

inline

Definition at line 722 of file fespace.hpp.

◆ GetDegenerateFaceDofs()

int mfem::FiniteElementSpace::GetDegenerateFaceDofs	(	int	index,
		Array< int > &	dofs,
		Geometry::Type	master_geom,
		int	variant ) const

protected

Definition at line 900 of file fespace.cpp.

◆ GetEdgeDofs()

int mfem::FiniteElementSpace::GetEdgeDofs	(	int	edge,
		Array< int > &	dofs,
		int	variant = 0 ) const

Returns the indices of the degrees of freedom for the specified edge, including the DOFs for the vertices of the edge.

In variable order spaces, multiple sets of DOFs may exist on an edge, corresponding to the different polynomial orders of incident elements. The 'variant' parameter is the zero-based index of the desired DOF set. The variants are ordered from lowest polynomial degree to the highest.

Returns: Order of the selected variant, or -1 if there are no more variants.

The returned indices are offsets into an ldof vector. See also GetEdgeVDofs().

Definition at line 3046 of file fespace.cpp.

◆ GetEdgeElement()

const FiniteElement * mfem::FiniteElementSpace::GetEdgeElement	(	int	i,
		int	variant = 0 ) const

Returns pointer to the FiniteElement in the FiniteElementCollection associated with i'th edge in the mesh object.

Definition at line 3267 of file fespace.cpp.

◆ GetEdgeInteriorDofs()

void mfem::FiniteElementSpace::GetEdgeInteriorDofs	(	int	i,
		Array< int > &	dofs ) const

Returns the indices of the degrees of freedom for the interior of the specified edge.

The returned indices are offsets into an ldof vector. See also GetEdgeInteriorVDofs().

Definition at line 3149 of file fespace.cpp.

◆ GetEdgeInteriorVDofs()

void mfem::FiniteElementSpace::GetEdgeInteriorVDofs	(	int	i,
		Array< int > &	vdofs ) const

Returns the indices of the degrees of freedom for the interior of the specified edge.

The returned indices are offsets into an ldof vector with vdim not necessarily equal to 1. See also GetEdgeInteriorDofs().

Definition at line 340 of file fespace.cpp.

◆ GetEdgeOrder()

int mfem::FiniteElementSpace::GetEdgeOrder	(	int	edge,
		int	variant = 0 ) const

Return the order of an edge. In a variable order space, return the order of a specific variant, or -1 if there are no more variants.

Definition at line 2699 of file fespace.cpp.

◆ GetEdgeVDofs()

void mfem::FiniteElementSpace::GetEdgeVDofs	(	int	i,
		Array< int > &	vdofs ) const

Returns the indices of the degrees of freedom for the specified edge, including the DOFs for the vertices of the edge.

The returned indices are offsets into an ldof vector with vdim not necessarily equal to 1. See GetEdgeDofs() for more information.

Definition at line 322 of file fespace.cpp.

◆ GetElementDofs() [1/2]

DofTransformation * mfem::FiniteElementSpace::GetElementDofs	(	int	elem,
		Array< int > &	dofs ) const

Returns indices of degrees of freedom of element 'elem'. The returned indices are offsets into an ldof vector. See also GetElementVDofs().

Note: In many cases the returned DofTransformation object will be NULL. In other cases see the documentation of the DofTransformation class for guidance on its role in performing edof to ldof transformations on local vectors and matrices. At present the DofTransformation is only needed for Nedelec basis functions of order 2 and above on 3D elements with triangular faces.; The returned object should NOT be deleted by the caller.

Definition at line 2846 of file fespace.cpp.

◆ GetElementDofs() [2/2]

void mfem::FiniteElementSpace::GetElementDofs	(	int	elem,
		Array< int > &	dofs,
		DofTransformation &	doftrans ) const

virtual

The same as GetElementDofs(), but with a user-allocated DofTransformation object. doftrans must be allocated in advance and will be owned by the caller. The user can use the DofTransformation::GetDofTransformation method on the returned doftrans object to detect if the DofTransformation should actually be used.

Reimplemented in mfem::ParFiniteElementSpace.

Definition at line 2738 of file fespace.cpp.

◆ GetElementForDof()

int mfem::FiniteElementSpace::GetElementForDof ( int i ) const

inline

Return the index of the first element that contains dof i.

This method can be called only after setup is performed using the method BuildDofToArrays().

Definition at line 1159 of file fespace.hpp.

◆ GetElementInteriorDofs()

void mfem::FiniteElementSpace::GetElementInteriorDofs	(	int	i,
		Array< int > &	dofs ) const

Returns the indices of the degrees of freedom for the interior of the specified element.

Specifically this refers to degrees of freedom which are not associated with the vertices, edges, or faces of the mesh. This method may be useful in conjunction with schemes which process shared and non-shared degrees of freedom differently such as static condensation.

The returned indices are offsets into an ldof vector. See also GetElementInteriorVDofs().

Definition at line 3104 of file fespace.cpp.

◆ GetElementInteriorVDofs()

void mfem::FiniteElementSpace::GetElementInteriorVDofs	(	int	i,
		Array< int > &	vdofs ) const

Returns the indices of the degrees of freedom for the interior of the specified element.

The returned indices are offsets into an ldof vector with vdim not necessarily equal to 1. See GetElementInteriorDofs() for more information.

Definition at line 334 of file fespace.cpp.

◆ GetElementOrder()

int mfem::FiniteElementSpace::GetElementOrder ( int i ) const

Returns the order of the i'th finite element.

Definition at line 176 of file fespace.cpp.

◆ GetElementOrderImpl()

int mfem::FiniteElementSpace::GetElementOrderImpl ( int i ) const

protected

Return element order: internal version of GetElementOrder without checks.

Definition at line 187 of file fespace.cpp.

◆ GetElementRestriction()

const ElementRestrictionOperator * mfem::FiniteElementSpace::GetElementRestriction ( ElementDofOrdering e_ordering ) const

Return an Operator that converts L-vectors to E-vectors.

An L-vector is a vector of size GetVSize() which is the same size as a GridFunction. An E-vector represents the element-wise discontinuous version of the FE space.

The layout of the E-vector is: ND x VDIM x NE, where ND is the number of degrees of freedom, VDIM is the vector dimension of the FE space, and NE is the number of the mesh elements.

The parameter e_ordering describes how the local DOFs in each element should be ordered in the E-vector, see ElementDofOrdering.

For discontinuous spaces, the element restriction corresponds to a permutation of the degrees of freedom, implemented by the L2ElementRestriction class.

The returned Operator is owned by the FiniteElementSpace.

Definition at line 1336 of file fespace.cpp.

◆ GetElementToDofTable()

const Table & mfem::FiniteElementSpace::GetElementToDofTable ( ) const

inline

Return a reference to the internal Table that stores the lists of scalar dofs, for each mesh element, as returned by GetElementDofs().

Definition at line 1136 of file fespace.hpp.

◆ GetElementToFaceOrientationTable()

const Table * mfem::FiniteElementSpace::GetElementToFaceOrientationTable ( ) const

inline

Definition at line 1132 of file fespace.hpp.

◆ GetElementTransformation() [1/2]

ElementTransformation * mfem::FiniteElementSpace::GetElementTransformation ( int i ) const

inline

Returns ElementTransformation for the i-th element.

Definition at line 773 of file fespace.hpp.

◆ GetElementTransformation() [2/2]

void mfem::FiniteElementSpace::GetElementTransformation	(	int	i,
		IsoparametricTransformation *	ElTr )

inline

Returns the transformation defining the i-th element in the user-defined variable ElTr.

Definition at line 778 of file fespace.hpp.

◆ GetElementType()

int mfem::FiniteElementSpace::GetElementType ( int i ) const

inline

Returns the type of element i.

Definition at line 761 of file fespace.hpp.

◆ GetElementVDofs() [1/2]

DofTransformation * mfem::FiniteElementSpace::GetElementVDofs	(	int	i,
		Array< int > &	vdofs ) const

Returns indices of degrees of freedom for the i'th element. The returned indices are offsets into an ldof vector with vdim not necessarily equal to 1. The returned indices are always ordered byNODES, irrespective of whether the space is byNODES or byVDIM. See also GetElementDofs().

Note: In many cases the returned DofTransformation object will be NULL. In other cases see the documentation of the DofTransformation class for guidance on its role in performing edof to ldof transformations on local vectors and matrices. At present the DofTransformation is only needed for Nedelec basis functions of order 2 and above on 3D elements with triangular faces.; The returned object should NOT be deleted by the caller.

Definition at line 287 of file fespace.cpp.

◆ GetElementVDofs() [2/2]

void mfem::FiniteElementSpace::GetElementVDofs	(	int	i,
		Array< int > &	vdofs,
		DofTransformation &	doftrans ) const

The same as GetElementVDofs(), but with a user-allocated DofTransformation object. doftrans must be allocated in advance and will be owned by the caller. The user can use the DofTransformation::GetDofTransformation method on the returned doftrans object to detect if the DofTransformation should actually be used.

Definition at line 278 of file fespace.cpp.

◆ GetElementVertices()

void mfem::FiniteElementSpace::GetElementVertices	(	int	i,
		Array< int > &	vertices ) const

inline

Returns the vertices of element i.

Definition at line 765 of file fespace.hpp.

◆ GetEntityDofs()

int mfem::FiniteElementSpace::GetEntityDofs	(	int	entity,
		int	index,
		Array< int > &	dofs,
		Geometry::Type	master_geom = Geometry::INVALID,
		int	variant = 0 ) const

protected

Helper to get vertex, edge or face DOFs (entity=0,1,2 resp.).

Definition at line 951 of file fespace.cpp.

◆ GetEntityVDofs()

int mfem::FiniteElementSpace::GetEntityVDofs	(	int	entity,
		int	index,
		Array< int > &	dofs,
		Geometry::Type	master_geom = Geometry::INVALID,
		int	variant = 0 ) const

protected

Helper to get vertex, edge or face VDOFs (entity=0,1,2 resp.).

Definition at line 976 of file fespace.cpp.

◆ GetEssentialTrueDofs()

void mfem::FiniteElementSpace::GetEssentialTrueDofs	(	const Array< int > &	bdr_attr_is_ess,
		Array< int > &	ess_tdof_list,
		int	component = -1 ) const

virtual

Get a list of essential true dofs, ess_tdof_list, corresponding to the boundary attributes marked in the array bdr_attr_is_ess. For spaces with 'vdim' > 1, the 'component' parameter can be used to restricts the marked tDOFs to the specified component.

Reimplemented in mfem::ParFiniteElementSpace.

Definition at line 588 of file fespace.cpp.

◆ GetEssentialVDofs()

void mfem::FiniteElementSpace::GetEssentialVDofs	(	const Array< int > &	bdr_attr_is_ess,
		Array< int > &	ess_vdofs,
		int	component = -1 ) const

virtual

Mark degrees of freedom associated with boundary elements with the specified boundary attributes (marked in 'bdr_attr_is_ess'). For spaces with 'vdim' > 1, the 'component' parameter can be used to restricts the marked vDOFs to the specified component.

Reimplemented in mfem::ParFiniteElementSpace.

Definition at line 514 of file fespace.cpp.

◆ GetFaceDofs()

int mfem::FiniteElementSpace::GetFaceDofs	(	int	face,
		Array< int > &	dofs,
		int	variant = 0 ) const

virtual

Returns the indices of the degrees of freedom for the specified face, including the DOFs for the edges and the vertices of the face.

In variable order spaces, multiple variants of DOFs can be returned. See GetEdgeDofs() for more details.

Returns: Order of the selected variant, or -1 if there are no more variants.

The returned indices are offsets into an ldof vector. See also GetFaceVDofs().

Reimplemented in mfem::ParFiniteElementSpace.

Definition at line 2958 of file fespace.cpp.

◆ GetFaceElement()

const FiniteElement * mfem::FiniteElementSpace::GetFaceElement ( int i ) const

Returns pointer to the FiniteElement in the FiniteElementCollection associated with i'th face in the mesh object. Faces in this case refer to the MESHDIM-1 primitive so in 2D they are segments and in 1D they are points.

Definition at line 3237 of file fespace.cpp.

◆ GetFaceInteriorDofs()

void mfem::FiniteElementSpace::GetFaceInteriorDofs	(	int	i,
		Array< int > &	dofs ) const

Returns the indices of the degrees of freedom for the interior of the specified face.

Specifically this refers to degrees of freedom which are not associated with the vertices, edges, or cell interiors of the mesh. This method may be useful in conjunction with schemes which process shared and non-shared degrees of freedom differently such as static condensation.

The returned indices are offsets into an ldof vector. See also GetFaceInteriorVDofs().

Definition at line 3125 of file fespace.cpp.

◆ GetFaceOrder()

int mfem::FiniteElementSpace::GetFaceOrder	(	int	face,
		int	variant = 0 ) const

Returns the polynomial degree of the i'th face finite element.

Definition at line 2710 of file fespace.cpp.

◆ GetFaceQuadratureInterpolator()

const FaceQuadratureInterpolator * mfem::FiniteElementSpace::GetFaceQuadratureInterpolator	(	const IntegrationRule &	ir,
		FaceType	type ) const

Return a FaceQuadratureInterpolator that interpolates E-vectors to quadrature point values and/or derivatives (Q-vectors).

Note: The returned pointer is shared. A good practice, before using it, is to set all its properties to their expected values, as other parts of the code may also change them. That is, it's good to call SetOutputLayout() and DisableTensorProducts() before interpolating.

Definition at line 1433 of file fespace.cpp.

◆ GetFaceRestriction()

const FaceRestriction * mfem::FiniteElementSpace::GetFaceRestriction	(	ElementDofOrdering	f_ordering,
		FaceType	type,
		L2FaceValues	mul = L2FaceValues::DoubleValued ) const

virtual

Return an Operator that converts L-vectors to E-vectors on each face.

Reimplemented in mfem::ParFiniteElementSpace.

Definition at line 1369 of file fespace.cpp.

◆ GetFaceToDofTable()

const Table & mfem::FiniteElementSpace::GetFaceToDofTable ( ) const

inline

Return a reference to the internal Table that stores the lists of scalar dofs, for each face in the mesh, as returned by GetFaceDofs(). In this context, "face" refers to a (dim-1)-dimensional mesh entity.

Note: In the case of a NURBS space, the rows corresponding to interior faces will be empty.

Definition at line 1149 of file fespace.hpp.

◆ GetFaceVDofs()

void mfem::FiniteElementSpace::GetFaceVDofs	(	int	i,
		Array< int > &	vdofs ) const

Returns the indices of the degrees of freedom for the specified face, including the DOFs for the edges and the vertices of the face.

The returned indices are offsets into an ldof vector with vdim not necessarily equal to 1. See GetFaceDofs() for more information.

Definition at line 316 of file fespace.cpp.

◆ GetFE()

const FiniteElement * mfem::FiniteElementSpace::GetFE ( int i ) const

virtual

Returns pointer to the FiniteElement in the FiniteElementCollection associated with i'th element in the mesh object. Note: The method has been updated to abort instead of returning NULL for an empty partition.

Reimplemented in mfem::ParFiniteElementSpace.

Definition at line 3168 of file fespace.cpp.

◆ GetHpConformingRestriction()

const SparseMatrix * mfem::FiniteElementSpace::GetHpConformingRestriction ( ) const

The returned SparseMatrix is owned by the FiniteElementSpace.

Return a version of the conforming restriction matrix for variable-order spaces with complex hp interfaces, where some true DOFs are not owned by any elements and need to be interpolated from higher order edge/face variants (see also SetRelaxedHpConformity()).

Definition at line 1317 of file fespace.cpp.

◆ GetHpRestrictionMatrix()

virtual const SparseMatrix * mfem::FiniteElementSpace::GetHpRestrictionMatrix ( ) const

inlinevirtual

The returned SparseMatrix is owned by the FiniteElementSpace.

Definition at line 624 of file fespace.hpp.

◆ GetLocalDerefinementMatrices()

void mfem::FiniteElementSpace::GetLocalDerefinementMatrices	(	Geometry::Type	geom,
		DenseTensor &	localR ) const

protected

Definition at line 2071 of file fespace.cpp.

◆ GetLocalDofForDof()

int mfem::FiniteElementSpace::GetLocalDofForDof ( int i ) const

inline

Return the local dof index in the first element that contains dof i.

This method can be called only after setup is performed using the method BuildDofToArrays().

Definition at line 1163 of file fespace.hpp.

◆ GetLocalRefinementMatrices() [1/2]

void mfem::FiniteElementSpace::GetLocalRefinementMatrices	(	const FiniteElementSpace &	coarse_fes,
		Geometry::Type	geom,
		DenseTensor &	localP ) const

protected

Return in localP the local refinement matrices that map between fespaces after mesh refinement.

This method assumes that this->mesh is a refinement of coarse_fes->mesh and that the CoarseFineTransformations of this->mesh are set accordingly. Another assumption is that the FEs of this use the same MapType as the FEs of coarse_fes. Finally, it assumes that the spaces this and coarse_fes are NOT variable-order spaces.

Definition at line 2171 of file fespace.cpp.

◆ GetLocalRefinementMatrices() [2/2]

void mfem::FiniteElementSpace::GetLocalRefinementMatrices	(	Geometry::Type	geom,
		DenseTensor &	localP ) const

protected

Definition at line 1528 of file fespace.cpp.

◆ GetMaxElementOrder()

int mfem::FiniteElementSpace::GetMaxElementOrder ( ) const

inline

Return the maximum polynomial order.

Definition at line 577 of file fespace.hpp.

◆ GetMesh()

Mesh * mfem::FiniteElementSpace::GetMesh ( ) const

inline

Returns the mesh.

Definition at line 559 of file fespace.hpp.

◆ GetNBE()

int mfem::FiniteElementSpace::GetNBE ( ) const

inline

Returns number of boundary elements in the mesh.

Definition at line 749 of file fespace.hpp.

◆ GetNConformingDofs()

int mfem::FiniteElementSpace::GetNConformingDofs ( ) const

Returns the number of conforming ("true") degrees of freedom (if the space is on a nonconforming mesh with hanging nodes).

Definition at line 1330 of file fespace.cpp.

◆ GetNDofs()

int mfem::FiniteElementSpace::GetNDofs ( ) const

inline

Returns number of degrees of freedom. This is the number of Local Degrees of Freedom.

Definition at line 710 of file fespace.hpp.

◆ GetNE()

int mfem::FiniteElementSpace::GetNE ( ) const

inline

Returns number of elements in the mesh.

Definition at line 740 of file fespace.hpp.

◆ GetNEDofs()

int mfem::FiniteElementSpace::GetNEDofs ( ) const

inline

Number of all scalar edge-interior dofs.

Definition at line 732 of file fespace.hpp.

◆ GetNF()

int mfem::FiniteElementSpace::GetNF ( ) const

inline

Returns number of faces (i.e. co-dimension 1 entities) in the mesh.

The co-dimension 1 entities are those that have dimension 1 less than the mesh dimension, e.g. for a 2D mesh, the faces are the 1D entities, i.e. the edges.

Definition at line 746 of file fespace.hpp.

◆ GetNFbyType()

int mfem::FiniteElementSpace::GetNFbyType ( FaceType type ) const

inline

Returns the number of faces according to the requested type.

If type==Boundary returns only the "true" number of boundary faces contrary to GetNBE() that returns "fake" boundary faces associated to visualization for GLVis. Similarly, if type==Interior, the "fake" boundary faces associated to visualization are counted as interior faces.

Definition at line 757 of file fespace.hpp.

◆ GetNFDofs()

int mfem::FiniteElementSpace::GetNFDofs ( ) const

inline

Number of all scalar face-interior dofs.

Definition at line 734 of file fespace.hpp.

◆ GetNumBorderDofs()

int mfem::FiniteElementSpace::GetNumBorderDofs	(	Geometry::Type	geom,
		int	order ) const

protected

Definition at line 942 of file fespace.cpp.

◆ GetNumElementInteriorDofs()

int mfem::FiniteElementSpace::GetNumElementInteriorDofs ( int i ) const

Returns the number of degrees of freedom associated with the interior of the specified element.

See GetElementInteriorDofs() for more information or to obtain the relevant indices.

Definition at line 3119 of file fespace.cpp.

◆ GetNURBSext() [1/2]

NURBSExtension * mfem::FiniteElementSpace::GetNURBSext ( )

inline

Definition at line 562 of file fespace.hpp.

◆ GetNURBSext() [2/2]

const NURBSExtension * mfem::FiniteElementSpace::GetNURBSext ( ) const

inline

Definition at line 561 of file fespace.hpp.

◆ GetNV()

int mfem::FiniteElementSpace::GetNV ( ) const

inline

Returns number of vertices in the mesh.

Definition at line 737 of file fespace.hpp.

◆ GetNVariants()

int mfem::FiniteElementSpace::GetNVariants	(	int	entity,
		int	index ) const

protected

Return number of possible DOF variants for edge/face (var. order spaces).

Definition at line 2726 of file fespace.cpp.

◆ GetNVDofs()

int mfem::FiniteElementSpace::GetNVDofs ( ) const

inline

Number of all scalar vertex dofs.

Definition at line 730 of file fespace.hpp.

◆ GetOrder()

int mfem::FiniteElementSpace::GetOrder ( int i ) const

inline

Returns the polynomial degree of the i'th finite element.

NOTE: it is recommended to use GetElementOrder in new code.

Definition at line 696 of file fespace.hpp.

◆ GetOrdering()

Ordering::Type mfem::FiniteElementSpace::GetOrdering ( ) const

inline

Return the ordering method.

Definition at line 725 of file fespace.hpp.

◆ GetPatchDofs()

void mfem::FiniteElementSpace::GetPatchDofs	(	int	patch,
		Array< int > &	dofs ) const

Returns indices of degrees of freedom for NURBS patch index patch. Cartesian ordering is used, for the tensor-product degrees of freedom.

Definition at line 3161 of file fespace.cpp.

◆ GetPatchVDofs()

void mfem::FiniteElementSpace::GetPatchVDofs	(	int	i,
		Array< int > &	vdofs ) const

Returns indices of degrees of freedom in vdofs for NURBS patch i.

Definition at line 310 of file fespace.cpp.

◆ GetProlongationMatrix()

virtual const Operator * mfem::FiniteElementSpace::GetProlongationMatrix ( ) const

inlinevirtual

The returned Operator is owned by the FiniteElementSpace.

Reimplemented in mfem::ceed::AlgebraicCoarseSpace, mfem::ceed::ParAlgebraicCoarseSpace, and mfem::ParFiniteElementSpace.

Definition at line 597 of file fespace.hpp.

◆ GetQuadratureInterpolator() [1/2]

const QuadratureInterpolator * mfem::FiniteElementSpace::GetQuadratureInterpolator ( const IntegrationRule & ir ) const

Return a QuadratureInterpolator that interpolates E-vectors to quadrature point values and/or derivatives (Q-vectors).

An E-vector represents the element-wise discontinuous version of the FE space and can be obtained, for example, from a GridFunction using the Operator returned by GetElementRestriction().

All elements will use the same IntegrationRule, ir as the target quadrature points.

Note: The returned pointer is shared. A good practice, before using it, is to set all its properties to their expected values, as other parts of the code may also change them. That is, it's good to call SetOutputLayout() and DisableTensorProducts() before interpolating.

Definition at line 1404 of file fespace.cpp.

◆ GetQuadratureInterpolator() [2/2]

const QuadratureInterpolator * mfem::FiniteElementSpace::GetQuadratureInterpolator ( const QuadratureSpace & qs ) const

Return a QuadratureInterpolator that interpolates E-vectors to quadrature point values and/or derivatives (Q-vectors).

An E-vector represents the element-wise discontinuous version of the FE space and can be obtained, for example, from a GridFunction using the Operator returned by GetElementRestriction().

The target quadrature points in the elements are described by the given QuadratureSpace, qs.

Note: The returned pointer is shared. A good practice, before using it, is to set all its properties to their expected values, as other parts of the code may also change them. That is, it's good to call SetOutputLayout() and DisableTensorProducts() before interpolating.

Definition at line 1418 of file fespace.cpp.

◆ GetRestrictionMatrix()

virtual const SparseMatrix * mfem::FiniteElementSpace::GetRestrictionMatrix ( ) const

inlinevirtual

The returned SparseMatrix is owned by the FiniteElementSpace.

Reimplemented in mfem::ceed::AlgebraicCoarseSpace, mfem::ceed::ParAlgebraicCoarseSpace, and mfem::ParFiniteElementSpace.

Definition at line 620 of file fespace.hpp.

◆ GetRestrictionOperator()

virtual const Operator * mfem::FiniteElementSpace::GetRestrictionOperator ( ) const

inlinevirtual

An abstract operator that performs the same action as GetRestrictionMatrix.

In some cases this is an optimized matrix-free implementation. The returned operator is owned by the FiniteElementSpace.

Reimplemented in mfem::ParFiniteElementSpace.

Definition at line 616 of file fespace.hpp.

◆ GetRestrictionTransposeOperator()

const Operator * mfem::FiniteElementSpace::GetRestrictionTransposeOperator ( ) const

Return an operator that performs the transpose of GetRestrictionOperator.

The returned operator is owned by the FiniteElementSpace.

For a serial conforming space, this returns NULL, indicating the identity operator.

For a parallel conforming space, this will return a matrix-free (Device)ConformingProlongationOperator.

For a non-conforming mesh this will return a TransposeOperator wrapping the restriction matrix.

Definition at line 1324 of file fespace.cpp.

◆ GetSequence()

long mfem::FiniteElementSpace::GetSequence ( ) const

inline

Return update counter, similar to Mesh::GetSequence(). Used by GridFunction to check if it is up to date with the space.

Definition at line 1310 of file fespace.hpp.

◆ GetTraceElement()

const FiniteElement * mfem::FiniteElementSpace::GetTraceElement	(	int	i,
		Geometry::Type	geom_type ) const

Return the trace element from element 'i' to the given 'geom_type'.

Definition at line 3276 of file fespace.cpp.

◆ GetTransferOperator()

void mfem::FiniteElementSpace::GetTransferOperator	(	const FiniteElementSpace &	coarse_fes,
		OperatorHandle &	T ) const

Construct and return an Operator that can be used to transfer GridFunction data from coarse_fes, defined on a coarse mesh, to this FE space, defined on a refined mesh.

It is assumed that the mesh of this FE space is a refinement of the mesh of coarse_fes and the CoarseFineTransformations returned by the method Mesh::GetRefinementTransforms() of the refined mesh are set accordingly. The Operator::Type of T can be set to request an Operator of the set type. Currently, only Operator::MFEM_SPARSEMAT and Operator::ANY_TYPE (matrix-free) are supported. When Operator::ANY_TYPE is requested, the choice of the particular Operator sub-class is left to the method. This method also works in parallel because the transfer operator is local to the MPI task when the input is a synchronized ParGridFunction.

Definition at line 3349 of file fespace.cpp.

◆ GetTrueTransferOperator()

void mfem::FiniteElementSpace::GetTrueTransferOperator	(	const FiniteElementSpace &	coarse_fes,
		OperatorHandle &	T ) const

virtual

Construct and return an Operator that can be used to transfer true-dof data from coarse_fes, defined on a coarse mesh, to this FE space, defined on a refined mesh.

This method calls GetTransferOperator() and multiplies the result by the prolongation operator of coarse_fes on the right, and by the restriction operator of this FE space on the left.

The Operator::Type of T can be set to request an Operator of the set type. In serial, the supported types are: Operator::MFEM_SPARSEMAT and Operator::ANY_TYPE (matrix-free). In parallel, the supported types are: Operator::Hypre_ParCSR and Operator::ANY_TYPE. Any other type is treated as Operator::ANY_TYPE: the operator representation choice is made by this method.

Reimplemented in mfem::ParFiniteElementSpace.

Definition at line 3376 of file fespace.cpp.

◆ GetTrueVSize()

virtual int mfem::FiniteElementSpace::GetTrueVSize ( ) const

inlinevirtual

Return the number of vector true (conforming) dofs.

Reimplemented in mfem::ParFiniteElementSpace.

Definition at line 716 of file fespace.hpp.

◆ GetUpdateOperator() [1/2]

const Operator * mfem::FiniteElementSpace::GetUpdateOperator ( )

inline

Get the GridFunction update operator.

Definition at line 1285 of file fespace.hpp.

◆ GetUpdateOperator() [2/2]

void mfem::FiniteElementSpace::GetUpdateOperator ( OperatorHandle & T )

inline

Return the update operator in the given OperatorHandle, T.

Definition at line 1288 of file fespace.hpp.

◆ GetVDim()

int mfem::FiniteElementSpace::GetVDim ( ) const

inline

Returns vector dimension.

Definition at line 706 of file fespace.hpp.

◆ GetVDofs()

void mfem::FiniteElementSpace::GetVDofs	(	int	vd,
		Array< int > &	dofs,
		int	ndofs = -1 ) const

Returns the indices of all of the VDofs for the specified dimension 'vd'.

The ndofs parameter can be used to indicate the total number of Dofs associated with each component of vdim. If ndofs is -1 (the default value), then the number of Dofs is determined by the FiniteElementSpace::GetNDofs().

Note: This method does not resize the dofs array. It takes the range of dofs [0, dofs.Size()) and converts these to vdofs and stores the results in the dofs array.

Definition at line 193 of file fespace.cpp.

◆ GetVertexDofs()

void mfem::FiniteElementSpace::GetVertexDofs	(	int	i,
		Array< int > &	dofs ) const

Returns the indices of the degrees of freedom for the specified vertices.

The returned indices are offsets into an ldof vector. See also GetVertexVDofs().

Definition at line 3094 of file fespace.cpp.

◆ GetVertexVDofs()

void mfem::FiniteElementSpace::GetVertexVDofs	(	int	i,
		Array< int > &	vdofs ) const

Returns the indices of the degrees of freedom for the specified vertices.

The returned indices are offsets into an ldof vector with vdim not necessarily equal to 1. See also GetVertexDofs().

Definition at line 328 of file fespace.cpp.

◆ GetVSize()

int mfem::FiniteElementSpace::GetVSize ( ) const

inline

Return the number of vector dofs, i.e. GetNDofs() x GetVDim().

Definition at line 713 of file fespace.hpp.

◆ H2L_GlobalRestrictionMatrix()

SparseMatrix * mfem::FiniteElementSpace::H2L_GlobalRestrictionMatrix ( FiniteElementSpace * lfes )

Construct the restriction matrix from the FE space given by (*this) to the lower degree FE space given by (*lfes) which is defined on the same mesh.

Definition at line 760 of file fespace.cpp.

◆ IsDGSpace()

bool mfem::FiniteElementSpace::IsDGSpace ( ) const

inline

Return whether or not the space is discontinuous (L2)

Definition at line 1313 of file fespace.hpp.

◆ IsVariableOrder()

bool mfem::FiniteElementSpace::IsVariableOrder ( ) const

inline

Returns true if the space contains elements of varying polynomial orders.

Definition at line 581 of file fespace.hpp.

◆ ListToMarker()

void mfem::FiniteElementSpace::ListToMarker	(	const Array< int > &	list,
		int	marker_size,
		Array< int > &	marker,
		int	mark_val = -1 )

static

Convert an array of indices (list) to a Boolean marker array where all indices in the list are marked with the given value and the rest are set to zero.

Definition at line 667 of file fespace.cpp.

◆ Load()

FiniteElementCollection * mfem::FiniteElementSpace::Load	(	Mesh *	m,
		std::istream &	input )

Read a FiniteElementSpace from a stream. The returned FiniteElementCollection is owned by the caller.

Definition at line 3618 of file fespace.cpp.

◆ MakeDofTable()

int mfem::FiniteElementSpace::MakeDofTable	(	int	ent_dim,
		const Array< int > &	entity_orders,
		Table &	entity_dofs,
		Array< char > *	var_ent_order )

protected

Build the table var_edge_dofs (or var_face_dofs) in a variable order space; return total edge/face DOFs.

Definition at line 2629 of file fespace.cpp.

◆ MakeVDimMatrix()

void mfem::FiniteElementSpace::MakeVDimMatrix ( SparseMatrix & mat ) const

protected

Replicate 'mat' in the vector dimension, according to vdim ordering mode.

Definition at line 1274 of file fespace.cpp.

◆ MarkerToList()

void mfem::FiniteElementSpace::MarkerToList	(	const Array< int > &	marker,
		Array< int > &	list )

static

Convert a Boolean marker array to a list containing all marked indices.

Definition at line 648 of file fespace.cpp.

◆ MinOrder()

int mfem::FiniteElementSpace::MinOrder ( VarOrderBits bits )

staticprotected

Return the minimum order (least significant bit set) in the bit mask.

Definition at line 2503 of file fespace.cpp.

◆ Nonconforming()

bool mfem::FiniteElementSpace::Nonconforming ( ) const

inline

Definition at line 566 of file fespace.hpp.

◆ operator=()

FiniteElementSpace & mfem::FiniteElementSpace::operator= ( const FiniteElementSpace & )

delete

Copy assignment not supported.

◆ RebuildElementToDofTable()

void mfem::FiniteElementSpace::RebuildElementToDofTable ( )

(

Deprecated: ) Use the Update() method if the space or mesh changed.

Definition at line 452 of file fespace.cpp.

◆ RefinementMatrix()

SparseMatrix * mfem::FiniteElementSpace::RefinementMatrix	(	int	old_ndofs,
		const Table *	old_elem_dof,
		const Table *	old_elem_fos )

protected

Calculate explicit GridFunction interpolation matrix (after mesh refinement). NOTE: consider using the RefinementOperator class instead of the fully assembled matrix, which can take a lot of memory.

Definition at line 1551 of file fespace.cpp.

◆ RefinementMatrix_main()

SparseMatrix * mfem::FiniteElementSpace::RefinementMatrix_main	(	const int	coarse_ndofs,
		const Table &	coarse_elem_dof,
		const Table *	coarse_elem_fos,
		const DenseTensor	localP[] ) const

protected

This method makes the same assumptions as the method: void GetLocalRefinementMatrices( const FiniteElementSpace &coarse_fes, Geometry::Type geom, DenseTensor &localP) const which is defined below. It also assumes that the coarse fes and this have the same vector dimension, vdim.

TODO: Implement DofTransformation support

Definition at line 1464 of file fespace.cpp.

◆ ReorderElementToDofTable()

void mfem::FiniteElementSpace::ReorderElementToDofTable ( )

Reorder the scalar DOFs based on the element ordering.

The new ordering is constructed as follows: 1) loop over all elements as ordered in the Mesh; 2) for each element, assign new indices to all of its current DOFs that are still unassigned; the new indices we assign are simply the sequence 0,1,2,...; if there are any signed DOFs their sign is preserved.

Definition at line 461 of file fespace.cpp.

◆ Save()

void mfem::FiniteElementSpace::Save ( std::ostream & out ) const

Save finite element space to output stream out.

Definition at line 3549 of file fespace.cpp.

◆ SetElementOrder()

void mfem::FiniteElementSpace::SetElementOrder	(	int	i,
		int	p )

Sets the order of the i'th finite element.

By default, all elements are assumed to be of fec->GetOrder(). Once SetElementOrder is called, the space becomes a variable order space.

Definition at line 149 of file fespace.cpp.

◆ SetRelaxedHpConformity()

void mfem::FiniteElementSpace::SetRelaxedHpConformity ( bool relaxed = true )

inline

In variable order spaces on nonconforming (NC) meshes, this function controls whether strict conformity is enforced in cases where coarse edges/faces have higher polynomial order than their fine NC neighbors. In the default (strict) case, the coarse side polynomial order is reduced to that of the lowest order fine edge/face, so all fine neighbors can interpolate the coarse side exactly. If relaxed == true, some discontinuities in the solution in such cases are allowed and the coarse side is not restricted. For an example, see https://github.com/mfem/mfem/pull/1423#issuecomment-621340392

Definition at line 1327 of file fespace.hpp.

◆ SetUpdateOperatorOwner()

void mfem::FiniteElementSpace::SetUpdateOperatorOwner ( bool own )

inline

Set the ownership of the update operator: if set to false, the Operator returned by GetUpdateOperator() must be deleted outside the FiniteElementSpace.

The update operator ownership is automatically reset to true when a new update operator is created by the Update() method.

Definition at line 1295 of file fespace.hpp.

◆ SetUpdateOperatorType()

void mfem::FiniteElementSpace::SetUpdateOperatorType ( Operator::Type tid )

inline

Specify the Operator::Type to be used by the update operators.

The default type is Operator::ANY_TYPE which leaves the choice to this class. The other currently supported option is Operator::MFEM_SPARSEMAT which is only guaranteed to be honored for a refinement update operator. Any other type will be treated as Operator::ANY_TYPE.

Note: This operation destroys the current update operator (if owned).

Definition at line 1303 of file fespace.hpp.

◆ StealNURBSext()

NURBSExtension * mfem::FiniteElementSpace::StealNURBSext ( )

Definition at line 2290 of file fespace.cpp.

◆ Update()

void mfem::FiniteElementSpace::Update ( bool want_transform = true )

virtual

Reflect changes in the mesh: update number of DOFs, etc. Also, calculate GridFunction transformation operator (unless want_transform is false). Safe to call multiple times, does nothing if space already up to date.

Reimplemented in mfem::ParFiniteElementSpace.

Definition at line 3439 of file fespace.cpp.

◆ UpdateElementOrders()

void mfem::FiniteElementSpace::UpdateElementOrders ( )

protected

Resize the elem_order array on mesh change.

Definition at line 3417 of file fespace.cpp.

◆ UpdateMeshPointer()

void mfem::FiniteElementSpace::UpdateMeshPointer ( Mesh * new_mesh )

protectedvirtual

Updates the internal mesh pointer.

Warning: new_mesh must be topologically identical to the existing mesh. Used if the address of the Mesh object has changed, e.g. in Mesh::Swap.

Definition at line 3544 of file fespace.cpp.

◆ UpdateNURBS()

void mfem::FiniteElementSpace::UpdateNURBS ( )

protected

Definition at line 2301 of file fespace.cpp.

◆ UpdatesFinished()

virtual void mfem::FiniteElementSpace::UpdatesFinished ( )

inlinevirtual

Free the GridFunction update operator (if any), to save memory.

Reimplemented in mfem::ParFiniteElementSpace.

Definition at line 1306 of file fespace.hpp.

◆ VDofToDof()

int mfem::FiniteElementSpace::VDofToDof ( int vdof ) const

inline

Compute the inverse of the Dof to VDof mapping for a single index vdof.

Warning: This method is only intended for use with positive indices. Passing a negative value for vdof will produce an invalid result.

Definition at line 995 of file fespace.hpp.

Friends And Related Symbol Documentation

◆ InterpolationGridTransfer

friend class InterpolationGridTransfer

friend

Definition at line 221 of file fespace.hpp.

◆ LORBase

friend class LORBase

friend

Definition at line 224 of file fespace.hpp.

◆ Mesh::Swap

void Mesh::Swap	(	Mesh &	,
		bool	)

friend

◆ PRefinementTransferOperator

friend class PRefinementTransferOperator

friend

Definition at line 222 of file fespace.hpp.

Member Data Documentation

◆ bdofs

int* mfem::FiniteElementSpace::bdofs

protected

internal DOFs of elements if mixed/var-order; NULL otherwise

Definition at line 250 of file fespace.hpp.

◆ bdr_elem_dof

Table* mfem::FiniteElementSpace::bdr_elem_dof

mutableprotected

Definition at line 264 of file fespace.hpp.

◆ bdr_elem_fos

Table* mfem::FiniteElementSpace::bdr_elem_fos

mutableprotected

Definition at line 265 of file fespace.hpp.

◆ cP

std::unique_ptr<SparseMatrix> mfem::FiniteElementSpace::cP

mutableprotected

Matrix representing the prolongation from the global conforming dofs to a set of intermediate partially conforming dofs, e.g. the dofs associated with a "cut" space on a non-conforming mesh.

Definition at line 280 of file fespace.hpp.

◆ cP_is_set

bool mfem::FiniteElementSpace::cP_is_set

mutableprotected

Definition at line 285 of file fespace.hpp.

◆ cR

std::unique_ptr<SparseMatrix> mfem::FiniteElementSpace::cR

mutableprotected

Conforming restriction matrix such that cR.cP=I.

Definition at line 282 of file fespace.hpp.

◆ cR_hp

std::unique_ptr<SparseMatrix> mfem::FiniteElementSpace::cR_hp

mutableprotected

A version of the conforming restriction matrix for variable-order spaces.

Definition at line 284 of file fespace.hpp.

◆ dof_elem_array

Array<int> mfem::FiniteElementSpace::dof_elem_array

protected

Definition at line 268 of file fespace.hpp.

◆ dof_ldof_array

Array<int> mfem::FiniteElementSpace::dof_ldof_array

protected

Definition at line 268 of file fespace.hpp.

◆ DoFTrans

DofTransformation mfem::FiniteElementSpace::DoFTrans

mutableprotected

Definition at line 275 of file fespace.hpp.

◆ DoFTransArray

Array<StatelessDofTransformation *> mfem::FiniteElementSpace::DoFTransArray

protected

Definition at line 274 of file fespace.hpp.

◆ E2BFQ_array

Array<FaceQuadratureInterpolator*> mfem::FiniteElementSpace::E2BFQ_array

mutableprotected

Definition at line 311 of file fespace.hpp.

◆ E2IFQ_array

Array<FaceQuadratureInterpolator*> mfem::FiniteElementSpace::E2IFQ_array

mutableprotected

Definition at line 310 of file fespace.hpp.

◆ E2Q_array

Array<QuadratureInterpolator*> mfem::FiniteElementSpace::E2Q_array

mutableprotected

Definition at line 309 of file fespace.hpp.

◆ elem_dof

Table* mfem::FiniteElementSpace::elem_dof

mutableprotected

Definition at line 262 of file fespace.hpp.

◆ elem_fos

Table* mfem::FiniteElementSpace::elem_fos

mutableprotected

Definition at line 263 of file fespace.hpp.

◆ elem_order

Array<char> mfem::FiniteElementSpace::elem_order

protected

Polynomial order for each element. If empty, all elements are assumed to be of the default order (fec->GetOrder()).

Definition at line 246 of file fespace.hpp.

◆ face_dof

Table* mfem::FiniteElementSpace::face_dof

mutableprotected

Definition at line 266 of file fespace.hpp.

◆ face_to_be

Array<int> mfem::FiniteElementSpace::face_to_be

mutableprotected

Definition at line 272 of file fespace.hpp.

◆ fec

const FiniteElementCollection* mfem::FiniteElementSpace::fec

protected

Associated FE collection (not owned).

Definition at line 231 of file fespace.hpp.

◆ L2E_lex

OperatorHandle mfem::FiniteElementSpace::L2E_lex

protected

Definition at line 293 of file fespace.hpp.

◆ L2E_nat

OperatorHandle mfem::FiniteElementSpace::L2E_nat

mutableprotected

The element restriction operators, see GetElementRestriction().

Definition at line 293 of file fespace.hpp.

◆ L2F

map_L2F mfem::FiniteElementSpace::L2F

mutableprotected

Definition at line 307 of file fespace.hpp.

◆ MaxVarOrder

int mfem::FiniteElementSpace::MaxVarOrder = 8*sizeof(VarOrderBits) - 1

staticconstexprprotected

Definition at line 346 of file fespace.hpp.

◆ mesh

Mesh* mfem::FiniteElementSpace::mesh

protected

The mesh that FE space lives on (not owned).

Definition at line 228 of file fespace.hpp.

◆ mesh_sequence

long mfem::FiniteElementSpace::mesh_sequence

protected

Mesh sequence number last seen when constructing the space. The space needs updating if Mesh::GetSequence() is larger than this.

Definition at line 319 of file fespace.hpp.

◆ nbdofs

int mfem::FiniteElementSpace::nbdofs

protected

Definition at line 248 of file fespace.hpp.

◆ ndofs

int mfem::FiniteElementSpace::ndofs

protected

Number of degrees of freedom. Number of unknowns is ndofs * vdim.

Definition at line 242 of file fespace.hpp.

◆ nedofs

int mfem::FiniteElementSpace::nedofs

protected

Definition at line 248 of file fespace.hpp.

◆ nfdofs

int mfem::FiniteElementSpace::nfdofs

protected

Definition at line 248 of file fespace.hpp.

◆ NURBSext

NURBSExtension* mfem::FiniteElementSpace::NURBSext

protected

Definition at line 270 of file fespace.hpp.

◆ nvdofs

int mfem::FiniteElementSpace::nvdofs

protected

Definition at line 248 of file fespace.hpp.

◆ ordering

Ordering::Type mfem::FiniteElementSpace::ordering

protected

Type of ordering of the vector dofs when vdim > 1.

Ordering::byNODES - first nodes, then vector dimension,
Ordering::byVDIM - first vector dimension, then nodes

Definition at line 239 of file fespace.hpp.

◆ orders_changed

bool mfem::FiniteElementSpace::orders_changed

protected

True if at least one element order changed (variable-order space only).

Definition at line 322 of file fespace.hpp.

◆ own_ext

int mfem::FiniteElementSpace::own_ext

protected

Definition at line 271 of file fespace.hpp.

◆ R_transpose

std::unique_ptr<Operator> mfem::FiniteElementSpace::R_transpose

mutableprotected

Operator computing the action of the transpose of the restriction.

Definition at line 287 of file fespace.hpp.

◆ relaxed_hp

bool mfem::FiniteElementSpace::relaxed_hp

protected

Definition at line 324 of file fespace.hpp.

◆ sequence

long mfem::FiniteElementSpace::sequence

protected

Update counter, incremented every time the space is constructed/updated. Used by GridFunctions to check if they are up to date with the space.

Definition at line 315 of file fespace.hpp.

◆ Th

OperatorHandle mfem::FiniteElementSpace::Th

protected

Transformation to apply to GridFunctions after space Update().

Definition at line 290 of file fespace.hpp.

◆ uni_fdof

int mfem::FiniteElementSpace::uni_fdof

protected

of single face DOFs if all faces uniform; -1 otherwise

Definition at line 249 of file fespace.hpp.

◆ var_edge_dofs

Table mfem::FiniteElementSpace::var_edge_dofs

protected

Variable order spaces only: DOF assignments for edges and faces, see docs in MakeDofTable. For constant order spaces the tables are empty.

Definition at line 254 of file fespace.hpp.

◆ var_edge_orders

Array<char> mfem::FiniteElementSpace::var_edge_orders

protected

Additional data for the var_*_dofs tables: individual variant orders (these are basically alternate J arrays for var_edge/face_dofs).

Definition at line 259 of file fespace.hpp.

◆ var_face_dofs

Table mfem::FiniteElementSpace::var_face_dofs

protected

NOTE: also used for spaces with mixed faces.

Definition at line 255 of file fespace.hpp.

◆ var_face_orders

Array<char> mfem::FiniteElementSpace::var_face_orders

protected

Definition at line 259 of file fespace.hpp.

◆ vdim

int mfem::FiniteElementSpace::vdim

protected

Vector dimension (number of unknowns per degree of freedom).

Definition at line 234 of file fespace.hpp.

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

fem/fespace.hpp
fem/fespace.cpp

Classes

Public Member Functions

Static Public Member Functions

Protected Types

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Static Protected Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ key_face

◆ map_L2F

◆ VarOrderBits

Constructor & Destructor Documentation

◆ FiniteElementSpace() [1/4]

◆ FiniteElementSpace() [2/4]

◆ FiniteElementSpace() [3/4]

◆ FiniteElementSpace() [4/4]

◆ ~FiniteElementSpace()

Member Function Documentation

◆ AddDependencies()

◆ AddEdgeFaceDependencies()

◆ AdjustVDofs()

◆ BuildBdrElementToDofTable()

◆ BuildConformingInterpolation()

◆ BuildDofToArrays()

◆ BuildElementToDofTable()

◆ BuildFaceToDofTable()

◆ BuildNURBSFaceToDofTable()

◆ CalcEdgeFaceVarOrders()

◆ Conforming()

◆ Construct()

◆ ConstructDoFTransArray()

◆ Constructor()

◆ ConvertFromConformingVDofs()

◆ ConvertToConformingVDofs()

◆ CopyProlongationAndRestriction()

◆ D2C_GlobalRestrictionMatrix()

◆ D2Const_GlobalRestrictionMatrix()

◆ DecodeDof() [1/2]

◆ DecodeDof() [2/2]

◆ DerefinementMatrix()

◆ Destroy()

◆ DestroyDoFTransArray()

◆ DofFinalizable()

◆ DofsToVDofs() [1/2]

◆ DofsToVDofs() [2/2]

◆ DofToVDof()

◆ EncodeDof()

◆ FEColl()

◆ FindDofs()

◆ FindEdgeDof()

◆ FindFaceDof()

◆ FirstFaceDof()

◆ GetAttribute()

◆ GetBdrAttribute()

◆ GetBdrElementDofs() [1/2]

◆ GetBdrElementDofs() [2/2]

◆ GetBdrElementToDofTable()

◆ GetBdrElementTransformation()

◆ GetBdrElementType()

◆ GetBdrElementVDofs() [1/2]

◆ GetBdrElementVDofs() [2/2]

◆ GetBE()

◆ GetBoundaryTrueDofs()

◆ GetConformingProlongation()

◆ GetConformingRestriction()

◆ GetConformingVSize()

◆ GetDegenerateFaceDofs()

◆ GetEdgeDofs()

◆ GetEdgeElement()

◆ GetEdgeInteriorDofs()

◆ GetEdgeInteriorVDofs()

◆ GetEdgeOrder()

◆ GetEdgeVDofs()

◆ GetElementDofs() [1/2]

◆ GetElementDofs() [2/2]

◆ GetElementForDof()

◆ GetElementInteriorDofs()