An arbitrary order and dimension NURBS element. More...

#include <fe_nurbs.hpp>

Inheritance diagram for mfem::NURBSFiniteElement:

Collaboration diagram for mfem::NURBSFiniteElement:

Public Member Functions
	NURBSFiniteElement (int D, Geometry::Type G, int Do, int O, int F)
	Construct NURBSFiniteElement with given.

void	Reset () const

void	SetIJK (const int *IJK) const

int	GetPatch () const

void	SetPatch (int p) const

int	GetElement () const

void	SetElement (int e) const

Array< const KnotVector * > &	KnotVectors () const

Vector &	Weights () const

virtual void	SetOrder () const
	Update the NURBSFiniteElement according to the currently set knot vectors.

const int *	GetIJK () const

Public Member Functions inherited from mfem::ScalarFiniteElement
	ScalarFiniteElement (int D, Geometry::Type G, int Do, int O, int F=FunctionSpace::Pk)
	Construct ScalarFiniteElement with given.

virtual void	SetMapType (int M)
	Set the FiniteElement::MapType of the element to either VALUE or INTEGRAL. Also sets the FiniteElement::DerivType to GRAD if the FiniteElement::MapType is VALUE.

void	NodalLocalInterpolation (ElementTransformation &Trans, DenseMatrix &I, const ScalarFiniteElement &fine_fe) const
	Get the matrix I that defines nodal interpolation between this element and the refined element fine_fe.

void	ScalarLocalInterpolation (ElementTransformation &Trans, DenseMatrix &I, const ScalarFiniteElement &fine_fe) const
	Get matrix I "Interpolation" defined through local L2-projection in the space defined by the fine_fe.

void	ScalarLocalL2Restriction (ElementTransformation &Trans, DenseMatrix &R, const ScalarFiniteElement &coarse_fe) const
	Get restriction matrix R defined through local L2-projection in the space defined by the coarse_fe.

Public Member Functions inherited from mfem::FiniteElement
	FiniteElement (int D, Geometry::Type G, int Do, int O, int F=FunctionSpace::Pk)
	Construct FiniteElement with given.

int	GetDim () const
	Returns the reference space dimension for the finite element.

int	GetRangeDim () const
	Returns the vector dimension for vector-valued finite elements, which is also the dimension of the interpolation operation.

int	GetCurlDim () const
	Returns the dimension of the curl for vector-valued finite elements.

Geometry::Type	GetGeomType () const
	Returns the Geometry::Type of the reference element.

int	GetDof () const
	Returns the number of degrees of freedom in the finite element.

int	GetOrder () const
	Returns the order of the finite element. In the case of anisotropic orders, returns the maximum order.

bool	HasAnisotropicOrders () const
	Returns true if the FiniteElement basis may be using different orders/degrees in different spatial directions.

const int *	GetAnisotropicOrders () const
	Returns an array containing the anisotropic orders/degrees.

int	Space () const
	Returns the type of FunctionSpace on the element.

int	GetRangeType () const
	Returns the FiniteElement::RangeType of the element, one of {SCALAR, VECTOR}.

int	GetDerivRangeType () const
	Returns the FiniteElement::RangeType of the element derivative, either SCALAR or VECTOR.

int	GetMapType () const
	Returns the FiniteElement::MapType of the element describing how reference functions are mapped to physical space, one of {VALUE, INTEGRAL H_DIV, H_CURL}.

int	GetDerivType () const
	Returns the FiniteElement::DerivType of the element describing the spatial derivative method implemented, one of {NONE, GRAD, DIV, CURL}.

int	GetDerivMapType () const
	Returns the FiniteElement::DerivType of the element describing how reference function derivatives are mapped to physical space, one of {VALUE, INTEGRAL, H_DIV, H_CURL}.

virtual void	CalcShape (const IntegrationPoint &ip, Vector &shape) const =0
	Evaluate the values of all shape functions of a scalar finite element in reference space at the given point ip.

void	CalcPhysShape (ElementTransformation &Trans, Vector &shape) const
	Evaluate the values of all shape functions of a scalar finite element in physical space at the point described by Trans.

virtual void	CalcDShape (const IntegrationPoint &ip, DenseMatrix &dshape) const =0
	Evaluate the gradients of all shape functions of a scalar finite element in reference space at the given point ip.

void	CalcPhysDShape (ElementTransformation &Trans, DenseMatrix &dshape) const
	Evaluate the gradients of all shape functions of a scalar finite element in physical space at the point described by Trans.

const IntegrationRule &	GetNodes () const
	Get a const reference to the nodes of the element.

virtual void	CalcVShape (const IntegrationPoint &ip, DenseMatrix &shape) const
	Evaluate the values of all shape functions of a vector finite element in reference space at the given point ip.

virtual void	CalcVShape (ElementTransformation &Trans, DenseMatrix &shape) const
	Evaluate the values of all shape functions of a vector finite element in physical space at the point described by Trans.

void	CalcPhysVShape (ElementTransformation &Trans, DenseMatrix &shape) const
	Equivalent to the CalcVShape() method with the same arguments.

virtual void	CalcDivShape (const IntegrationPoint &ip, Vector &divshape) const
	Evaluate the divergence of all shape functions of a vector finite element in reference space at the given point ip.

void	CalcPhysDivShape (ElementTransformation &Trans, Vector &divshape) const
	Evaluate the divergence of all shape functions of a vector finite element in physical space at the point described by Trans.

virtual void	CalcCurlShape (const IntegrationPoint &ip, DenseMatrix &curl_shape) const
	Evaluate the curl of all shape functions of a vector finite element in reference space at the given point ip.

virtual void	CalcPhysCurlShape (ElementTransformation &Trans, DenseMatrix &curl_shape) const
	Evaluate the curl of all shape functions of a vector finite element in physical space at the point described by Trans.

virtual void	GetFaceDofs (int face, int *dofs, int ndofs) const
	Get the dofs associated with the given face. dofs is set to an internal array of the local dofc on the face, while ndofs is set to the number of dofs on that face.

virtual void	CalcHessian (const IntegrationPoint &ip, DenseMatrix &Hessian) const
	Evaluate the Hessians of all shape functions of a scalar finite element in reference space at the given point ip.

virtual void	CalcPhysHessian (ElementTransformation &Trans, DenseMatrix &Hessian) const
	Evaluate the Hessian of all shape functions of a scalar finite element in reference space at the given point ip.

virtual void	CalcPhysLaplacian (ElementTransformation &Trans, Vector &Laplacian) const
	Evaluate the Laplacian of all shape functions of a scalar finite element in reference space at the given point ip.

virtual void	CalcPhysLinLaplacian (ElementTransformation &Trans, Vector &Laplacian) const

virtual void	GetLocalInterpolation (ElementTransformation &Trans, DenseMatrix &I) const
	Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base geometry under the given transformation.

virtual void	GetLocalRestriction (ElementTransformation &Trans, DenseMatrix &R) const
	Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs.

virtual void	GetTransferMatrix (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
	Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this finite element.

virtual void	Project (Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
	Given a coefficient and a transformation, compute its projection (approximation) in the local finite dimensional space in terms of the degrees of freedom.

virtual void	Project (VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
	Given a vector coefficient and a transformation, compute its projection (approximation) in the local finite dimensional space in terms of the degrees of freedom. (VectorFiniteElements)

virtual void	ProjectFromNodes (Vector &vc, ElementTransformation &Trans, Vector &dofs) const
	Given a vector of values at the finite element nodes and a transformation, compute its projection (approximation) in the local finite dimensional space in terms of the degrees of freedom. Valid for VectorFiniteElements.

virtual void	ProjectMatrixCoefficient (MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
	Given a matrix coefficient and a transformation, compute an approximation ("projection") in the local finite dimensional space in terms of the degrees of freedom. For VectorFiniteElements, the rows of the coefficient are projected in the vector space.

virtual void	ProjectDelta (int vertex, Vector &dofs) const
	Project a delta function centered on the given vertex in the local finite dimensional space represented by the dofs.

virtual void	Project (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
	Compute the embedding/projection matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the projection depends on it.

virtual void	ProjectGrad (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
	Compute the discrete gradient matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.

virtual void	ProjectCurl (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
	Compute the discrete curl matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.

virtual void	ProjectDiv (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &div) const
	Compute the discrete divergence matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.

virtual const DofToQuad &	GetDofToQuad (const IntegrationRule &ir, DofToQuad::Mode mode) const
	Return a DofToQuad structure corresponding to the given IntegrationRule using the given DofToQuad::Mode.

virtual void	GetFaceMap (const int face_id, Array< int > &face_map) const
	Return the mapping from lexicographic face DOFs to lexicographic element DOFs for the given local face face_id.

virtual const StatelessDofTransformation *	GetDofTransformation () const
	Return a DoF transformation object for this particular type of basis.

virtual	~FiniteElement ()
	Deconstruct the FiniteElement.

Protected Attributes
Array< const KnotVector * >	kv

const int *	ijk

int	patch

int	elem

Vector	weights

Protected Attributes inherited from mfem::FiniteElement
int	dim
	Dimension of reference space.

int	vdim
	Vector dimension of vector-valued basis functions.

int	cdim
	Dimension of curl for vector-valued basis functions.

Geometry::Type	geom_type
	Geometry::Type of the reference element.

int	func_space

int	range_type

int	map_type

int	deriv_type

int	deriv_range_type

int	deriv_map_type

int	dof
	Number of degrees of freedom.

int	order
	Order/degree of the shape functions.

int	orders [Geometry::MaxDim]
	Anisotropic orders.

IntegrationRule	Nodes

DenseMatrix	vshape

Array< DofToQuad * >	dof2quad_array
	Container for all DofToQuad objects created by the FiniteElement.

Additional Inherited Members
Public Types inherited from mfem::FiniteElement
enum	RangeType { UNKNOWN_RANGE_TYPE = -1 , SCALAR , VECTOR }
	Enumeration for range_type and deriv_range_type. More...

enum	MapType { UNKNOWN_MAP_TYPE = -1 , VALUE , INTEGRAL , H_DIV , H_CURL }
	Enumeration for MapType: defines how reference functions are mapped to physical space. More...

enum	DerivType { NONE , GRAD , DIV , CURL }
	Enumeration for DerivType: defines which derivative method is implemented. More...

Static Public Member Functions inherited from mfem::FiniteElement
static bool	IsClosedType (int b_type)
	Return true if the BasisType of b_type is closed (has Quadrature1D points on the boundary).

static bool	IsOpenType (int b_type)
	Return true if the BasisType of b_type is open (doesn't have Quadrature1D points on the boundary).

static int	VerifyClosed (int b_type)
	Ensure that the BasisType of b_type is closed (has Quadrature1D points on the boundary).

static int	VerifyOpen (int b_type)
	Ensure that the BasisType of b_type is open (doesn't have Quadrature1D points on the boundary).

static int	VerifyNodal (int b_type)
	Ensure that the BasisType of b_type nodal (satisfies the interpolation property).

Static Protected Member Functions inherited from mfem::ScalarFiniteElement
static const ScalarFiniteElement &	CheckScalarFE (const FiniteElement &fe)

Detailed Description

An arbitrary order and dimension NURBS element.

Definition at line 23 of file fe_nurbs.hpp.

Constructor & Destructor Documentation

◆ NURBSFiniteElement()

mfem::NURBSFiniteElement::NURBSFiniteElement	(	int	D,
		Geometry::Type	G,
		int	Do,
		int	O,
		int	F )

inline

Construct NURBSFiniteElement with given.

Parameters

D	Reference space dimension
G	Geometry type (of type Geometry::Type)
Do	Number of degrees of freedom in the FiniteElement
O	Order/degree of the FiniteElement
F	FunctionSpace type of the FiniteElement

Definition at line 39 of file fe_nurbs.hpp.

Member Function Documentation

◆ GetElement()

int mfem::NURBSFiniteElement::GetElement ( ) const

inline

Definition at line 53 of file fe_nurbs.hpp.

◆ GetIJK()

const int * mfem::NURBSFiniteElement::GetIJK ( ) const

inline

Returns the indices (i,j) in 2D or (i,j,k) in 3D of this element in the tensor product ordering of the patch.

Definition at line 62 of file fe_nurbs.hpp.

◆ GetPatch()

int mfem::NURBSFiniteElement::GetPatch ( ) const

inline

Definition at line 51 of file fe_nurbs.hpp.

◆ KnotVectors()

Array< const KnotVector * > & mfem::NURBSFiniteElement::KnotVectors ( ) const

inline

Definition at line 55 of file fe_nurbs.hpp.

◆ Reset()

void mfem::NURBSFiniteElement::Reset ( ) const

inline

Definition at line 49 of file fe_nurbs.hpp.

◆ SetElement()

void mfem::NURBSFiniteElement::SetElement ( int e ) const

inline

Definition at line 54 of file fe_nurbs.hpp.

◆ SetIJK()

void mfem::NURBSFiniteElement::SetIJK ( const int * IJK ) const

inline

Definition at line 50 of file fe_nurbs.hpp.

◆ SetOrder()

virtual void mfem::NURBSFiniteElement::SetOrder ( ) const

inlinevirtual

Update the NURBSFiniteElement according to the currently set knot vectors.

Reimplemented in mfem::NURBS1DFiniteElement, mfem::NURBS2DFiniteElement, and mfem::NURBS3DFiniteElement.

Definition at line 58 of file fe_nurbs.hpp.

◆ SetPatch()

void mfem::NURBSFiniteElement::SetPatch ( int p ) const

inline

Definition at line 52 of file fe_nurbs.hpp.

◆ Weights()

Vector & mfem::NURBSFiniteElement::Weights ( ) const

inline

Definition at line 56 of file fe_nurbs.hpp.

Member Data Documentation

◆ elem

int mfem::NURBSFiniteElement::elem

protected

Definition at line 28 of file fe_nurbs.hpp.

◆ ijk

const int* mfem::NURBSFiniteElement::ijk

mutableprotected

Definition at line 27 of file fe_nurbs.hpp.

◆ kv

Array<const KnotVector*> mfem::NURBSFiniteElement::kv

mutableprotected

Definition at line 26 of file fe_nurbs.hpp.

◆ patch

int mfem::NURBSFiniteElement::patch

mutableprotected

Definition at line 28 of file fe_nurbs.hpp.

◆ weights

Vector mfem::NURBSFiniteElement::weights

mutableprotected

Definition at line 29 of file fe_nurbs.hpp.

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

fem/fe/fe_nurbs.hpp

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ NURBSFiniteElement()

Member Function Documentation

◆ GetElement()

◆ GetIJK()

◆ GetPatch()

◆ KnotVectors()

◆ Reset()

◆ SetElement()

◆ SetIJK()

◆ SetOrder()

◆ SetPatch()

◆ Weights()

Member Data Documentation

◆ elem

◆ ijk

◆ kv

◆ patch

◆ weights