An arbitrary order 3D NURBS element on a cube. More...

#include <fe_nurbs.hpp>

Inheritance diagram for mfem::NURBS3DFiniteElement:

Collaboration diagram for mfem::NURBS3DFiniteElement:

Public Member Functions
	NURBS3DFiniteElement (int p)
	Construct the NURBS3DFiniteElement of order p.

	NURBS3DFiniteElement (int px, int py, int pz)

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

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

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

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.

Public Member Functions inherited from mfem::NURBSFiniteElement
	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

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}.

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.

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	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
Vector	u

Vector	shape_x

Vector	shape_y

Vector	shape_z

Vector	dshape_x

Vector	dshape_y

Vector	dshape_z

Vector	d2shape_x

Vector	d2shape_y

Vector	d2shape_z

DenseMatrix	du

Protected Attributes inherited from mfem::NURBSFiniteElement
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 3D NURBS element on a cube.

Definition at line 119 of file fe_nurbs.hpp.

Constructor & Destructor Documentation

◆ NURBS3DFiniteElement() [1/2]

mfem::NURBS3DFiniteElement::NURBS3DFiniteElement ( int p )

inline

Construct the NURBS3DFiniteElement of order p.

Definition at line 129 of file fe_nurbs.hpp.

◆ NURBS3DFiniteElement() [2/2]

mfem::NURBS3DFiniteElement::NURBS3DFiniteElement	(	int	px,
		int	py,
		int	pz )

inline

Construct the NURBS3DFiniteElement with x-order px and y-order py and z-order pz

Definition at line 139 of file fe_nurbs.hpp.

Member Function Documentation

◆ CalcDShape()

void mfem::NURBS3DFiniteElement::CalcDShape	(	const IntegrationPoint &	ip,
		DenseMatrix &	dshape ) const

virtual

Evaluate the gradients of all shape functions of a scalar finite element in reference space at the given point ip.

Each row of the result DenseMatrix dshape contains the derivatives of one shape function. The size (dof x dim) of dshape must be set in advance.

Implements mfem::FiniteElement.

Definition at line 267 of file fe_nurbs.cpp.

◆ CalcHessian()

void mfem::NURBS3DFiniteElement::CalcHessian	(	const IntegrationPoint &	ip,
		DenseMatrix &	Hessian ) const

virtual

Evaluate the Hessians of all shape functions of a scalar finite element in reference space at the given point ip.

Each row of the result DenseMatrix Hessian contains upper triangular part of the Hessian of one shape function. The order in 2D is {u_xx, u_xy, u_yy}. The size (dof x (dim (dim+1)/2) of Hessian must be set in advance.

Reimplemented from mfem::FiniteElement.

Definition at line 313 of file fe_nurbs.cpp.

◆ CalcShape()

void mfem::NURBS3DFiniteElement::CalcShape	(	const IntegrationPoint &	ip,
		Vector &	shape ) const

virtual

Evaluate the values of all shape functions of a scalar finite element in reference space at the given point ip.

The size (dof) of the result Vector shape must be set in advance.

Implements mfem::FiniteElement.

Definition at line 243 of file fe_nurbs.cpp.

◆ SetOrder()

void mfem::NURBS3DFiniteElement::SetOrder ( ) const

virtual

Update the NURBSFiniteElement according to the currently set knot vectors.

Reimplemented from mfem::NURBSFiniteElement.

Definition at line 219 of file fe_nurbs.cpp.

Member Data Documentation

◆ d2shape_x

Vector mfem::NURBS3DFiniteElement::d2shape_x

mutableprotected

Definition at line 124 of file fe_nurbs.hpp.

◆ d2shape_y

Vector mfem::NURBS3DFiniteElement::d2shape_y

protected

Definition at line 124 of file fe_nurbs.hpp.

◆ d2shape_z

Vector mfem::NURBS3DFiniteElement::d2shape_z

protected

Definition at line 124 of file fe_nurbs.hpp.

◆ dshape_x

Vector mfem::NURBS3DFiniteElement::dshape_x

mutableprotected

Definition at line 123 of file fe_nurbs.hpp.

◆ dshape_y

Vector mfem::NURBS3DFiniteElement::dshape_y

protected

Definition at line 123 of file fe_nurbs.hpp.

◆ dshape_z

Vector mfem::NURBS3DFiniteElement::dshape_z

protected

Definition at line 123 of file fe_nurbs.hpp.

◆ du

DenseMatrix mfem::NURBS3DFiniteElement::du

mutableprotected

Definition at line 125 of file fe_nurbs.hpp.

◆ shape_x

Vector mfem::NURBS3DFiniteElement::shape_x

protected

Definition at line 122 of file fe_nurbs.hpp.

◆ shape_y

Vector mfem::NURBS3DFiniteElement::shape_y

protected

Definition at line 122 of file fe_nurbs.hpp.

◆ shape_z

Vector mfem::NURBS3DFiniteElement::shape_z

protected

Definition at line 122 of file fe_nurbs.hpp.

◆ u

Vector mfem::NURBS3DFiniteElement::u

mutableprotected

Definition at line 122 of file fe_nurbs.hpp.

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

fem/fe/fe_nurbs.hpp
fem/fe/fe_nurbs.cpp

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ NURBS3DFiniteElement() [1/2]

◆ NURBS3DFiniteElement() [2/2]

Member Function Documentation

◆ CalcDShape()

◆ CalcHessian()

◆ CalcShape()

◆ SetOrder()

Member Data Documentation

◆ d2shape_x

◆ d2shape_y

◆ d2shape_z

◆ dshape_x

◆ dshape_y

◆ dshape_z

◆ du

◆ shape_x

◆ shape_y

◆ shape_z

◆ u