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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 elements in 2D on a triangle. More...
#include <fe_rt.hpp>
Public Member Functions | |
| RT_TriangleElement (const int p) | |
| Construct the RT_TriangleElement of order p. | |
| 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. | |
| 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 | 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 | 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 | 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 | 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 | 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 | 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::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::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 elements in 2D on a triangle.
| mfem::RT_TriangleElement::RT_TriangleElement | ( | const int | p | ) |
Construct the RT_TriangleElement of order p.
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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::FiniteElement.
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inlinevirtual |
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.
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inlinevirtual |
Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base geometry under the given transformation.
Reimplemented from mfem::FiniteElement.
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inlinevirtual |
Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs.
The fine element is the image of the base geometry under the given transformation, Trans.
The assumption in this method is that a subset of the coarse dofs can be expressed only in terms of the dofs of the given fine element.
Rows in R corresponding to coarse dofs that cannot be expressed in terms of the fine dofs will be marked as invalid by setting the first entry (column 0) in the row to infinity().
This method assumes that the dimensions of R are set before it is called.
Reimplemented from mfem::FiniteElement.
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inlinevirtual |
Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this finite element.
Trans represents the mapping from the reference element of this element into a subset of the reference space of the element fe, thus allowing the "coarse" FiniteElement to be different from the "fine" FiniteElement as when h-refinement is combined with p-refinement or p-derefinement. It is assumed that both finite elements use the same FiniteElement::MapType.
Reimplemented from mfem::FiniteElement.
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virtual |
Given a coefficient and a transformation, compute its projection (approximation) in the local finite dimensional space in terms of the degrees of freedom.
The approximation used to project is usually local interpolation of degrees of freedom. The derived class could use other methods not implemented yet, e.g. local L2 projection.
Reimplemented from mfem::FiniteElement.
Definition at line 523 of file fe_base.cpp.
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inlinevirtual |
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.
Reimplemented from mfem::FiniteElement.
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inlinevirtual |
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)
The approximation used to project is usually local interpolation of degrees of freedom. The derived class could use other methods not implemented yet, e.g. local L2 projection.
Reimplemented from mfem::FiniteElement.
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inlinevirtual |
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.
Reimplemented from mfem::FiniteElement.
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inlinevirtual |
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.
Reimplemented from mfem::FiniteElement.
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inlinevirtual |
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.
Reimplemented from mfem::FiniteElement.
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inlinevirtual |
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.
Reimplemented from mfem::FiniteElement.
1.11.0