MFEM  v4.2.0 Finite element discretization library
mfem::L2Pos_SegmentElement Class Reference

Arbitrary order L2 elements in 1D utilizing the Bernstein basis on a segment. More...

#include <fe.hpp>

Inheritance diagram for mfem::L2Pos_SegmentElement:
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Collaboration diagram for mfem::L2Pos_SegmentElement:
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## Public Member Functions

L2Pos_SegmentElement (const int p)
Construct the L2Pos_SegmentElement of order p. 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 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...

Public Member Functions inherited from mfem::PositiveTensorFiniteElement
PositiveTensorFiniteElement (const int dims, const int p, const DofMapType dmtype)

Return a DofToQuad structure corresponding to the given IntegrationRule using the given DofToQuad::Mode. More...

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. 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 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 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...

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...

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 IntegrationRuleGetNodes () 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 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. 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 GetLocalRestriction (ElementTransformation &Trans, DenseMatrix &R) const
Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs. More...

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 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...

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 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 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...

virtual ~FiniteElement ()
Deconstruct the FiniteElement. More...

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::BasisGetBasis1D () 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. More...

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...

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). 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...

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. More...

Public Attributes inherited from mfem::ScalarFiniteElement

G

Do

O

F

Protected Member Functions inherited from mfem::ScalarFiniteElement

Static Protected Member Functions inherited from mfem::ScalarFiniteElement
static const ScalarFiniteElementCheckScalarFE (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 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

Container for all DofToQuad objects created by the FiniteElement. More...

Protected Attributes inherited from mfem::TensorBasisElement
int b_type

Array< int > dof_map

Poly_1D::Basisbasis1d

Array< int > inv_dof_map

## Detailed Description

Arbitrary order L2 elements in 1D utilizing the Bernstein basis on a segment.

Definition at line 2442 of file fe.hpp.

## Constructor & Destructor Documentation

 mfem::L2Pos_SegmentElement::L2Pos_SegmentElement ( const int p )

Construct the L2Pos_SegmentElement of order p.

Definition at line 9464 of file fe.cpp.

## Member Function Documentation

 void mfem::L2Pos_SegmentElement::CalcDShape ( const IntegrationPoint & ip, DenseMatrix & dshape ) const
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 9491 of file fe.cpp.

 void mfem::L2Pos_SegmentElement::CalcShape ( const IntegrationPoint & ip, Vector & shape ) const
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 9485 of file fe.cpp.

 void mfem::L2Pos_SegmentElement::ProjectDelta ( int vertex, Vector & dofs ) const
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 9502 of file fe.cpp.

The documentation for this class was generated from the following files: