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MFEM v4.7.0
Finite element discretization library
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MFEM v4.7.0
Finite element discretization library
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Arbitrary order Raviart-Thomas 3D elements in 2D on a square. More...
#include <fe_rt.hpp>
Public Member Functions | |
| RT_R2D_QuadrilateralElement (const int p, const int cb_type=BasisType::GaussLobatto, const int ob_type=BasisType::GaussLegendre) | |
| Construct the RT_QuadrilateralElement of order p and closed and open BasisType cb_type and ob_type. | |
| 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 | 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. | |
| 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. | |
 Public Member Functions inherited from mfem::RT_R2D_FiniteElement | |
| 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 (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 | 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 | 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 | 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. | |
| 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 IntegrationRule & | GetNodes () const |
| Get a const reference to the nodes of the element. | |
| 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 | 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 | 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 | 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 | 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. | |
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::RT_R2D_FiniteElement | |
| RT_R2D_FiniteElement (int p, Geometry::Type G, int Do, const real_t *nk_fe) | |
| 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 VectorFiniteElement & | CheckVectorFE (const FiniteElement &fe) |
| Protected Attributes inherited from mfem::RT_R2D_FiniteElement | |
| const real_t * | nk |
| Array< int > | dof_map |
| Array< int > | dof2nk |
| 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. | |
Arbitrary order Raviart-Thomas 3D elements in 2D on a square.
| mfem::RT_R2D_QuadrilateralElement::RT_R2D_QuadrilateralElement | ( | const int | p, |
| const int | cb_type = BasisType::GaussLobatto, | ||
| const int | ob_type = BasisType::GaussLegendre ) |
Construct the RT_QuadrilateralElement of order p and closed and open BasisType cb_type and ob_type.
|
virtual |
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.
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virtual |
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::RT_R2D_FiniteElement.
|
virtual |
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::RT_R2D_FiniteElement.
1.11.0