 |
MFEM
v4.3.0
Finite element discretization library
|
|
MFEM
v4.3.0
Finite element discretization library
|
Arbitrary order H1 elements in 2D on a triangle. More...
#include <fe.hpp>
Public Member Functions | |
| H1_TriangleElement (const int p, const int btype=BasisType::GaussLobatto) | |
| Construct the H1_TriangleElement of order p and BasisType btype. More... | |
| 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. More... | |
| 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. More... | |
| virtual void | CalcHessian (const IntegrationPoint &ip, DenseMatrix &ddshape) const |
| Evaluate the Hessians of all shape functions of a scalar finite element in reference space at the given point ip. More... | |
 Public Member Functions inherited from mfem::NodalFiniteElement | |
| NodalFiniteElement (int D, Geometry::Type G, int Do, int O, int F=FunctionSpace::Pk) | |
| Construct NodalFiniteElement with given. More... | |
| 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. More... | |
| virtual void | GetLocalRestriction (ElementTransformation &Trans, DenseMatrix &R) const |
| Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs. More... | |
| 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. More... | |
| 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. More... | |
| 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) More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| const Array< int > & | GetLexicographicOrdering () const |
| Get an Array<int> that maps lexicographically ordered indices to the indices of the respective nodes/dofs/basis functions. Lexicographic ordering of nodes is defined in terms of reference-space coordinates (x,y,z). Lexicographically ordered nodes are listed first in order of increasing x-coordinate, and then in order of increasing y-coordinate, and finally in order of increasing z-coordinate. More... | |
| 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. More... | |
| c_shape (dof) | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| void | ScalarLocalRestriction (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. More... | |
| 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. More... | |
| 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. More... | |
| int | GetDim () const |
| Returns the reference space dimension for the finite element. More... | |
| Geometry::Type | GetGeomType () const |
| Returns the Geometry::Type of the reference element. More... | |
| int | GetDof () const |
| Returns the number of degrees of freedom in the finite element. More... | |
| int | GetOrder () const |
| Returns the order of the finite element. In the case of anisotropic orders, returns the maximum order. More... | |
| bool | HasAnisotropicOrders () const |
| Returns true if the FiniteElement basis may be using different orders/degrees in different spatial directions. More... | |
| const int * | GetAnisotropicOrders () const |
| Returns an array containing the anisotropic orders/degrees. More... | |
| int | Space () const |
| Returns the type of FunctionSpace on the element. More... | |
| int | GetRangeType () const |
| Returns the FiniteElement::RangeType of the element, one of {SCALAR, VECTOR}. More... | |
| int | GetDerivRangeType () const |
| Returns the FiniteElement::RangeType of the element derivative, either SCALAR or VECTOR. More... | |
| 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}. More... | |
| int | GetDerivType () const |
| Returns the FiniteElement::DerivType of the element describing the spatial derivative method implemented, one of {NONE, GRAD, DIV, CURL}. More... | |
| 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}. More... | |
| 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. More... | |
| 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. More... | |
| const IntegrationRule & | GetNodes () const |
| Get a const reference to the nodes of the element. More... | |
| 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. More... | |
| 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. More... | |
| void | CalcPhysVShape (ElementTransformation &Trans, DenseMatrix &shape) const |
| Equivalent to the CalcVShape() method with the same arguments. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| virtual | ~FiniteElement () |
| Deconstruct the FiniteElement. More... | |
Additional Inherited Members | |
| Public Types inherited from mfem::FiniteElement | |
| enum | RangeType { SCALAR, VECTOR } |
| Enumeration for range_type and deriv_range_type. More... | |
| enum | MapType { 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). More... | |
| static bool | IsOpenType (int b_type) |
| Return true if the BasisType of b_type is open (doesn't have Quadrature1D points on the boundary). More... | |
| static int | VerifyClosed (int b_type) |
| Ensure that the BasisType of b_type is closed (has Quadrature1D points on the boundary). More... | |
| static int | VerifyOpen (int b_type) |
| Ensure that the BasisType of b_type is open (doesn't have Quadrature1D points on the boundary). More... | |
| static int | VerifyNodal (int b_type) |
| Ensure that the BasisType of b_type nodal (satisfies the interpolation property). More... | |
| Public Attributes inherited from mfem::ScalarFiniteElement | |
| __pad0__: FiniteElement(D | |
| G | |
| Do | |
| O | |
| F | |
| Protected Member Functions inherited from mfem::NodalFiniteElement | |
| void | ProjectCurl_2D (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const |
| Protected Member Functions inherited from mfem::ScalarFiniteElement | |
| const DofToQuad & | GetTensorDofToQuad (const class TensorBasisElement &tb, const IntegrationRule &ir, DofToQuad::Mode mode) const |
| Static Protected Member Functions inherited from mfem::ScalarFiniteElement | |
| static const ScalarFiniteElement & | CheckScalarFE (const FiniteElement &fe) |
| Protected Attributes inherited from mfem::NodalFiniteElement | |
| Array< int > | lex_ordering |
| Protected Attributes inherited from mfem::ScalarFiniteElement | |
| Vector | c_shape |
| Protected Attributes inherited from mfem::FiniteElement | |
| int | dim |
| Dimension of reference space. More... | |
| Geometry::Type | geom_type |
| Geometry::Type of the reference element. More... | |
| 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. More... | |
| int | order |
| Order/degree of the shape functions. More... | |
| int | orders [Geometry::MaxDim] |
| Anisotropic orders. More... | |
| IntegrationRule | Nodes |
| DenseMatrix | vshape |
| Array< DofToQuad * > | dof2quad_array |
| Container for all DofToQuad objects created by the FiniteElement. More... | |
| mfem::H1_TriangleElement::H1_TriangleElement | ( | const int | p, |
| const int | btype = BasisType::GaussLobatto |
||
| ) |
Construct the H1_TriangleElement of order p and BasisType btype.
|
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.
|
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.
|
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.
1.8.5
