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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 H1 elements in 2D utilizing the Bernstein basis on a square. More...
#include <fe_pos.hpp>
Public Member Functions | |
| H1Pos_QuadrilateralElement (const int p) | |
| Construct the H1Pos_QuadrilateralElement of order p. | |
| 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 | 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. | |
 Public Member Functions inherited from mfem::PositiveTensorFiniteElement | |
| PositiveTensorFiniteElement (const int dims, const int p, const DofMapType dmtype) | |
| const DofToQuad & | GetDofToQuad (const IntegrationRule &ir, DofToQuad::Mode mode) const override |
| Return a DofToQuad structure corresponding to the given IntegrationRule using the given DofToQuad::Mode. | |
| void | GetFaceMap (const int face_id, Array< int > &face_map) const override |
| Return the mapping from lexicographic face DOFs to lexicographic element DOFs for the given local face face_id. | |
| Public Member Functions inherited from mfem::PositiveFiniteElement | |
| PositiveFiniteElement (int D, Geometry::Type G, int Do, int O, int F=FunctionSpace::Pk) | |
| Construct PositiveFiniteElement with given. | |
| 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 | 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. | |
| 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 | 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 | 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 StatelessDofTransformation * | GetDofTransformation () const |
| Return a DoF transformation object for this particular type of basis. | |
| virtual | ~FiniteElement () |
| Deconstruct the FiniteElement. | |
| Public Member Functions inherited from mfem::TensorBasisElement | |
| TensorBasisElement (const int dims, const int p, const int btype, const DofMapType dmtype) | |
| int | GetBasisType () const |
| const Poly_1D::Basis & | GetBasis1D () const |
| const Array< int > & | GetDofMap () const |
| Get an Array<int> that maps lexicographically ordered indices to the indices of the respective nodes/dofs/basis functions. If the dofs are ordered lexicographically, i.e. the mapping is identity, the returned Array will be empty. | |
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... | |
| Public Types inherited from mfem::TensorBasisElement | |
| enum | DofMapType { L2_DOF_MAP = 0 , H1_DOF_MAP = 1 , Sr_DOF_MAP = 2 } |
| 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 Public Member Functions inherited from mfem::TensorBasisElement | |
| static Geometry::Type | GetTensorProductGeometry (int dim) |
| static int | Pow (int base, int dim) |
| Return base raised to the power dim. | |
| static const DofToQuad & | GetTensorDofToQuad (const FiniteElement &fe, const IntegrationRule &ir, DofToQuad::Mode mode, const Poly_1D::Basis &basis, bool closed, Array< DofToQuad * > &dof2quad_array) |
| Static Protected Member Functions inherited from mfem::ScalarFiniteElement | |
| static const ScalarFiniteElement & | CheckScalarFE (const FiniteElement &fe) |
| 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::TensorBasisElement | |
| int | b_type |
| Array< int > | dof_map |
| Poly_1D::Basis & | basis1d |
| Array< int > | inv_dof_map |
Arbitrary order H1 elements in 2D utilizing the Bernstein basis on a square.
Definition at line 142 of file fe_pos.hpp.
| mfem::H1Pos_QuadrilateralElement::H1Pos_QuadrilateralElement | ( | const int | p | ) |
Construct the H1Pos_QuadrilateralElement of order p.
Definition at line 364 of file fe_pos.cpp.
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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 404 of file fe_pos.cpp.
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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 384 of file fe_pos.cpp.
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virtual |
Project a delta function centered on the given vertex in the local finite dimensional space represented by the dofs.
Reimplemented from mfem::FiniteElement.
Definition at line 425 of file fe_pos.cpp.
1.11.0