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MFEM
v4.1.0
Finite element discretization library
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MFEM
v4.1.0
Finite element discretization library
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Class for quadratic FE on triangle. More...
#include <fe.hpp>
Public Member Functions | |
| Quad2DFiniteElement () | |
| Construct a quadratic FE on triangle. More... | |
| virtual void | CalcShape (const IntegrationPoint &ip, Vector &shape) const |
| virtual void | CalcDShape (const IntegrationPoint &ip, DenseMatrix &dshape) const |
| virtual void | CalcHessian (const IntegrationPoint &ip, DenseMatrix &h) const |
| Evaluate the Hessians of all shape functions of a scalar finite element in reference space at the given point ip. More... | |
| virtual void | ProjectDelta (int vertex, Vector &dofs) const |
 Public Member Functions inherited from mfem::NodalFiniteElement | |
| NodalFiniteElement (int D, Geometry::Type G, int Do, int O, int F=FunctionSpace::Pk) | |
| 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 |
| virtual void | Project (VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const |
| virtual void | ProjectMatrixCoefficient (MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const |
| virtual void | Project (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const |
| virtual void | ProjectGrad (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const |
| virtual void | ProjectDiv (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &div) const |
| Public Member Functions inherited from mfem::ScalarFiniteElement | |
| ScalarFiniteElement (int D, Geometry::Type G, int Do, int O, int F=FunctionSpace::Pk) | |
| c_shape (Dof) | |
| void | SetMapType (int M) |
| void | NodalLocalInterpolation (ElementTransformation &Trans, DenseMatrix &I, const ScalarFiniteElement &fine_fe) const |
| Nodal interpolation. More... | |
| void | ScalarLocalInterpolation (ElementTransformation &Trans, DenseMatrix &I, const ScalarFiniteElement &fine_fe) const |
| "Interpolation" defined through local L2-projection. More... | |
| virtual const DofToQuad & | GetDofToQuad (const IntegrationRule &ir, DofToQuad::Mode mode) const |
| Public Member Functions inherited from mfem::FiniteElement | |
| FiniteElement (int D, Geometry::Type G, int Do, int O, int F=FunctionSpace::Pk) | |
| 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 space on each element. More... | |
| int | GetRangeType () const |
| int | GetDerivRangeType () const |
| int | GetMapType () const |
| int | GetDerivType () const |
| int | GetDerivMapType () const |
| 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 |
| 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 |
| 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 | ProjectCurl (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const |
| virtual | ~FiniteElement () |
Additional Inherited Members | |
| Public Types inherited from mfem::FiniteElement | |
| enum | { SCALAR, VECTOR } |
| Enumeration for RangeType and DerivRangeType. More... | |
| enum | { VALUE, INTEGRAL, H_DIV, H_CURL } |
| Enumeration for MapType: defines how reference functions are mapped to physical space. More... | |
| enum | { 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) |
| static bool | IsOpenType (int b_type) |
| static int | VerifyClosed (int b_type) |
| static int | VerifyOpen (int b_type) |
| static int | VerifyNodal (int b_type) |
| 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::ScalarFiniteElement | |
| Vector | c_shape |
| Protected Attributes inherited from mfem::FiniteElement | |
| int | Dim |
| Dimension of reference space. More... | |
| Geometry::Type | GeomType |
| Geometry::Type of the reference element. More... | |
| int | FuncSpace |
| int | RangeType |
| int | MapType |
| int | DerivType |
| int | DerivRangeType |
| int | DerivMapType |
| 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::Quad2DFiniteElement::Quad2DFiniteElement | ( | ) |
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virtual function which evaluates the values of all partial derivatives of all shape functions at a given point ip and stores them in the matrix dshape (Dof x Dim) (6 x 2) so that each row contains the derivatives of one shape function
Implements mfem::FiniteElement.
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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.
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virtual function which evaluates the values of all shape functions at a given point ip and stores them in the vector shape of dimension Dof (6)
Implements mfem::FiniteElement.
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Compute a representation (up to multiplicative constant) for the delta function at the vertex with the given index.
Reimplemented from mfem::FiniteElement.
1.8.5
