MFEM
v4.0
Finite element discretization library
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#include <fe.hpp>
Public Member Functions | |
ND_TriangleElement (const int 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. 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... | |
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... | |
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 (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 |
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VectorFiniteElement (int D, Geometry::Type G, int Do, int O, int M, int F=FunctionSpace::Pk) | |
FiniteElement (D, G, Do, O, F) | |
Jinv (D) | |
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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 |
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... | |
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 | CalcHessian (const IntegrationPoint &ip, DenseMatrix &h) const |
virtual void | Project (Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const |
virtual void | ProjectDelta (int vertex, Vector &dofs) const |
virtual void | ProjectCurl (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const |
virtual void | ProjectDiv (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &div) const |
virtual const DofToQuad & | GetDofToQuad (const IntegrationRule &ir, DofToQuad::Mode mode) const |
virtual | ~FiniteElement () |
Additional Inherited Members | |
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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... | |
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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) |
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void | SetDerivMembers () |
void | CalcVShape_RT (ElementTransformation &Trans, DenseMatrix &shape) const |
void | CalcVShape_ND (ElementTransformation &Trans, DenseMatrix &shape) const |
void | Project_RT (const double *nk, const Array< int > &d2n, VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const |
void | ProjectMatrixCoefficient_RT (const double *nk, const Array< int > &d2n, MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const |
void | Project_RT (const double *nk, const Array< int > &d2n, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const |
void | ProjectGrad_RT (const double *nk, const Array< int > &d2n, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const |
void | ProjectCurl_ND (const double *tk, const Array< int > &d2t, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const |
void | ProjectCurl_RT (const double *nk, const Array< int > &d2n, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const |
void | Project_ND (const double *tk, const Array< int > &d2t, VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const |
void | ProjectMatrixCoefficient_ND (const double *tk, const Array< int > &d2t, MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const |
void | Project_ND (const double *tk, const Array< int > &d2t, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const |
void | ProjectGrad_ND (const double *tk, const Array< int > &d2t, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const |
void | LocalInterpolation_RT (const VectorFiniteElement &cfe, const double *nk, const Array< int > &d2n, ElementTransformation &Trans, DenseMatrix &I) const |
void | LocalInterpolation_ND (const VectorFiniteElement &cfe, const double *tk, const Array< int > &d2t, ElementTransformation &Trans, DenseMatrix &I) const |
void | LocalRestriction_RT (const double *nk, const Array< int > &d2n, ElementTransformation &Trans, DenseMatrix &R) const |
void | LocalRestriction_ND (const double *tk, const Array< int > &d2t, ElementTransformation &Trans, DenseMatrix &R) const |
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static const VectorFiniteElement & | CheckVectorFE (const FiniteElement &fe) |
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DenseMatrix | J |
DenseMatrix | Jinv |
DenseMatrix | curlshape |
DenseMatrix | curlshape_J |
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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::ND_TriangleElement::ND_TriangleElement | ( | const int | p | ) |
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Evaluate the curl of all shape functions of a vector finite element in reference space at the given point ip.
Each row of the result DenseMatrix curl_shape contains the components of the curl of one vector shape function. The size (Dof x CDim) of curl_shape must be set in advance, where CDim = 3 for Dim = 3 and CDim = 1 for Dim = 2.
Reimplemented from mfem::FiniteElement.
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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 MapType.
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)
Reimplemented from mfem::FiniteElement.
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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 |
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.