MFEM v4.8.0
Finite element discretization library
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mfem::NURBS_HDiv3DFiniteElement Class Reference

#include <fe_nurbs.hpp>

Inheritance diagram for mfem::NURBS_HDiv3DFiniteElement:
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Collaboration diagram for mfem::NURBS_HDiv3DFiniteElement:
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Public Member Functions

 NURBS_HDiv3DFiniteElement (int p)
 Construct the NURBS_HDiv3DFiniteElement of order p.
 
 NURBS_HDiv3DFiniteElement (int px, int py, int pz)
 Construct the NURBS_HDiv3DFiniteElement with x-order px, y-order py and z-order pz.
 
void SetOrder () const override
 
void CalcVShape (const IntegrationPoint &ip, DenseMatrix &shape) const override
 Evaluate the values of all shape functions of a vector finite element in reference space at the given point ip.
 
void CalcVShape (ElementTransformation &Trans, DenseMatrix &shape) const override
 Evaluate the values of all shape functions of a vector finite element in physical space at the point described by Trans.
 
void CalcDivShape (const IntegrationPoint &ip, Vector &divshape) const override
 Evaluate the divergence of all shape functions of a vector finite element in reference space at the given point ip.
 
 ~NURBS_HDiv3DFiniteElement ()
 
- Public Member Functions inherited from mfem::VectorFiniteElement
 VectorFiniteElement (int D, Geometry::Type G, int Do, int O, int M, int F=FunctionSpace::Pk)
 
- 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 IntegrationRuleGetNodes () const
 Get a const reference to the nodes of the element.
 
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.
 
void CalcPhysHessian (ElementTransformation &Trans, DenseMatrix &Hessian) const
 Evaluate the Hessian of all shape functions of a scalar finite element in physical space at the given point ip.
 
void CalcPhysLaplacian (ElementTransformation &Trans, Vector &Laplacian) const
 Evaluate the Laplacian of all shape functions of a scalar finite element in physical space at the given point ip.
 
void CalcPhysLinLaplacian (ElementTransformation &Trans, Vector &Laplacian) const
 Evaluate the Laplacian of all shape functions of a scalar finite element in physical space at the given point ip.
 
void CalcPhysVShape (ElementTransformation &Trans, DenseMatrix &shape) const
 Equivalent to the CalcVShape() method with the same arguments.
 
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 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 DofToQuadGetDofToQuad (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 StatelessDofTransformationGetDofTransformation () const
 Return a DoF transformation object for this particular type of basis.
 
virtual ~FiniteElement ()
 Deconstruct the FiniteElement.
 
- Public Member Functions inherited from mfem::NURBSFiniteElement
 NURBSFiniteElement (int dim)
 Construct NURBSFiniteElement with given.
 
void Reset () const
 Resets the patch and element data stored in the element.
 
void SetIJK (const int *IJK) const
 Set which IJK in patch should be evaluated.
 
int GetPatch () const
 Get which patch is currently considered.
 
void SetPatch (int p) const
 Set which patch should be evaluated.
 
int GetElement () const
 Set which element should be evaluated.
 
void SetElement (int e) const
 Get which element is currently considered.
 
Array< const KnotVector * > & KnotVectors () const
 Get the KnotVectors.
 
VectorWeights () const
 Get the Weights.
 
const int * GetIJK () const
 

Protected Attributes

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
 
Vector shape1_x
 
Vector shape1_y
 
Vector shape1_z
 
Vector dshape1_x
 
Vector dshape1_y
 
Vector dshape1_z
 
Vector d2shape1_x
 
Vector d2shape1_y
 
Vector d2shape1_z
 
Vector u
 
DenseMatrix du
 
Array< const KnotVector * > kv1
 
- Protected Attributes inherited from mfem::VectorFiniteElement
bool is_nodal
 
DenseMatrix JtJ
 
DenseMatrix curlshape
 
DenseMatrix curlshape_J
 
- 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.
 
- Protected Attributes inherited from mfem::NURBSFiniteElement
Array< const KnotVector * > kv
 
const int * ijk
 
int patch
 
int elem
 
Vector weights
 

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).
 
- Protected Member Functions inherited from mfem::VectorFiniteElement
void SetDerivMembers ()
 
void CalcVShape_RT (ElementTransformation &Trans, DenseMatrix &shape) const
 
void CalcVShape_ND (ElementTransformation &Trans, DenseMatrix &shape) const
 
void Project_RT (const real_t *nk, const Array< int > &d2n, VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
 Project a vector coefficient onto the RT basis functions.
 
void Project_RT (const real_t *nk, const Array< int > &d2n, Vector &vc, ElementTransformation &Trans, Vector &dofs) const
 Projects the vector of values given at FE nodes to RT space.
 
void ProjectMatrixCoefficient_RT (const real_t *nk, const Array< int > &d2n, MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
 Project the rows of the matrix coefficient in an RT space.
 
void Project_RT (const real_t *nk, const Array< int > &d2n, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
 Project vector-valued basis functions onto the RT basis functions.
 
void ProjectGrad_RT (const real_t *nk, const Array< int > &d2n, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
 
void ProjectCurl_ND (const real_t *tk, const Array< int > &d2t, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
 
void ProjectCurl_RT (const real_t *nk, const Array< int > &d2n, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
 
void Project_ND (const real_t *tk, const Array< int > &d2t, VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
 Project a vector coefficient onto the ND basis functions.
 
void Project_ND (const real_t *tk, const Array< int > &d2t, Vector &vc, ElementTransformation &Trans, Vector &dofs) const
 Projects the vector of values given at FE nodes to ND space.
 
void ProjectMatrixCoefficient_ND (const real_t *tk, const Array< int > &d2t, MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
 Project the rows of the matrix coefficient in an ND space.
 
void Project_ND (const real_t *tk, const Array< int > &d2t, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
 Project vector-valued basis functions onto the ND basis functions.
 
void ProjectGrad_ND (const real_t *tk, const Array< int > &d2t, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
 
void LocalL2Projection_RT (const VectorFiniteElement &cfe, ElementTransformation &Trans, DenseMatrix &I) const
 
void LocalInterpolation_RT (const VectorFiniteElement &cfe, const real_t *nk, const Array< int > &d2n, ElementTransformation &Trans, DenseMatrix &I) const
 
void LocalL2Projection_ND (const VectorFiniteElement &cfe, ElementTransformation &Trans, DenseMatrix &I) const
 
void LocalInterpolation_ND (const VectorFiniteElement &cfe, const real_t *tk, const Array< int > &d2t, ElementTransformation &Trans, DenseMatrix &I) const
 
void LocalRestriction_RT (const real_t *nk, const Array< int > &d2n, ElementTransformation &Trans, DenseMatrix &R) const
 
void LocalRestriction_ND (const real_t *tk, const Array< int > &d2t, ElementTransformation &Trans, DenseMatrix &R) const
 
- Static Protected Member Functions inherited from mfem::VectorFiniteElement
static const VectorFiniteElementCheckVectorFE (const FiniteElement &fe)
 

Detailed Description

An arbitrary order H(div)-conforming 3D NURBS element on a cube More details in the following papers:

[1] Annalisa Buffa, Carlo De Falco, Giancarlo Sangalli "Isogeometric analysis: stable elements for the 2D Stokes equation." International Journal for Numerical Methods in Fluids 65 (11‐12) 1407-1422

[2] John A Evans, Thomas JR Hughes "Isogeometric divergence-conforming B-splines for the unsteady Navier–Stokes equations." Journal of Computational Physics (241) 141-167

Definition at line 260 of file fe_nurbs.hpp.

Constructor & Destructor Documentation

◆ NURBS_HDiv3DFiniteElement() [1/2]

mfem::NURBS_HDiv3DFiniteElement::NURBS_HDiv3DFiniteElement ( int p)
inline

Construct the NURBS_HDiv3DFiniteElement of order p.

Definition at line 276 of file fe_nurbs.hpp.

◆ NURBS_HDiv3DFiniteElement() [2/2]

mfem::NURBS_HDiv3DFiniteElement::NURBS_HDiv3DFiniteElement ( int px,
int py,
int pz )
inline

Construct the NURBS_HDiv3DFiniteElement with x-order px, y-order py and z-order pz.

Definition at line 296 of file fe_nurbs.hpp.

◆ ~NURBS_HDiv3DFiniteElement()

mfem::NURBS_HDiv3DFiniteElement::~NURBS_HDiv3DFiniteElement ( )

Definition at line 699 of file fe_nurbs.cpp.

Member Function Documentation

◆ CalcDivShape()

void mfem::NURBS_HDiv3DFiniteElement::CalcDivShape ( const IntegrationPoint & ip,
Vector & divshape ) const
overridevirtual

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

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

Reimplemented from mfem::FiniteElement.

Definition at line 647 of file fe_nurbs.cpp.

◆ CalcVShape() [1/2]

void mfem::NURBS_HDiv3DFiniteElement::CalcVShape ( const IntegrationPoint & ip,
DenseMatrix & shape ) const
overridevirtual

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

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

Reimplemented from mfem::FiniteElement.

Definition at line 574 of file fe_nurbs.cpp.

◆ CalcVShape() [2/2]

void mfem::NURBS_HDiv3DFiniteElement::CalcVShape ( ElementTransformation & Trans,
DenseMatrix & shape ) const
overridevirtual

Evaluate the values of all shape functions of a vector finite element in physical space at the point described by Trans.

Each row of the result DenseMatrix shape contains the components of one vector shape function. The size (dof x SDim) of shape must be set in advance, where SDim >= dim is the physical space dimension as described by Trans.

Reimplemented from mfem::FiniteElement.

Definition at line 627 of file fe_nurbs.cpp.

◆ SetOrder()

void mfem::NURBS_HDiv3DFiniteElement::SetOrder ( ) const
overridevirtual

Update the polynomial order according to the currently set knotvectors Resizes all internal data members to have the correct size related to the polynomial order

Reimplemented from mfem::NURBSFiniteElement.

Definition at line 527 of file fe_nurbs.cpp.

Member Data Documentation

◆ d2shape1_x

Vector mfem::NURBS_HDiv3DFiniteElement::d2shape1_x
mutableprotected

Definition at line 269 of file fe_nurbs.hpp.

◆ d2shape1_y

Vector mfem::NURBS_HDiv3DFiniteElement::d2shape1_y
protected

Definition at line 269 of file fe_nurbs.hpp.

◆ d2shape1_z

Vector mfem::NURBS_HDiv3DFiniteElement::d2shape1_z
protected

Definition at line 269 of file fe_nurbs.hpp.

◆ d2shape_x

Vector mfem::NURBS_HDiv3DFiniteElement::d2shape_x
mutableprotected

Definition at line 266 of file fe_nurbs.hpp.

◆ d2shape_y

Vector mfem::NURBS_HDiv3DFiniteElement::d2shape_y
protected

Definition at line 266 of file fe_nurbs.hpp.

◆ d2shape_z

Vector mfem::NURBS_HDiv3DFiniteElement::d2shape_z
protected

Definition at line 266 of file fe_nurbs.hpp.

◆ dshape1_x

Vector mfem::NURBS_HDiv3DFiniteElement::dshape1_x
mutableprotected

Definition at line 268 of file fe_nurbs.hpp.

◆ dshape1_y

Vector mfem::NURBS_HDiv3DFiniteElement::dshape1_y
protected

Definition at line 268 of file fe_nurbs.hpp.

◆ dshape1_z

Vector mfem::NURBS_HDiv3DFiniteElement::dshape1_z
protected

Definition at line 268 of file fe_nurbs.hpp.

◆ dshape_x

Vector mfem::NURBS_HDiv3DFiniteElement::dshape_x
mutableprotected

Definition at line 265 of file fe_nurbs.hpp.

◆ dshape_y

Vector mfem::NURBS_HDiv3DFiniteElement::dshape_y
protected

Definition at line 265 of file fe_nurbs.hpp.

◆ dshape_z

Vector mfem::NURBS_HDiv3DFiniteElement::dshape_z
protected

Definition at line 265 of file fe_nurbs.hpp.

◆ du

DenseMatrix mfem::NURBS_HDiv3DFiniteElement::du
mutableprotected

Definition at line 271 of file fe_nurbs.hpp.

◆ kv1

Array<const KnotVector*> mfem::NURBS_HDiv3DFiniteElement::kv1
mutableprotected

Definition at line 272 of file fe_nurbs.hpp.

◆ shape1_x

Vector mfem::NURBS_HDiv3DFiniteElement::shape1_x
mutableprotected

Definition at line 267 of file fe_nurbs.hpp.

◆ shape1_y

Vector mfem::NURBS_HDiv3DFiniteElement::shape1_y
protected

Definition at line 267 of file fe_nurbs.hpp.

◆ shape1_z

Vector mfem::NURBS_HDiv3DFiniteElement::shape1_z
protected

Definition at line 267 of file fe_nurbs.hpp.

◆ shape_x

Vector mfem::NURBS_HDiv3DFiniteElement::shape_x
mutableprotected

Definition at line 264 of file fe_nurbs.hpp.

◆ shape_y

Vector mfem::NURBS_HDiv3DFiniteElement::shape_y
protected

Definition at line 264 of file fe_nurbs.hpp.

◆ shape_z

Vector mfem::NURBS_HDiv3DFiniteElement::shape_z
protected

Definition at line 264 of file fe_nurbs.hpp.

◆ u

Vector mfem::NURBS_HDiv3DFiniteElement::u
mutableprotected

Definition at line 270 of file fe_nurbs.hpp.


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