Public Member Functions
Sundance::Nedelec Class Reference

Lowest-order Nedelec basis. More...

Inheritance diagram for Sundance::Nedelec:
Sundance::HCurlVectorBasis Sundance::VectorBasis Sundance::BasisFamilyBase Sundance::Handleable< BasisFamilyBase > Sundance::Printable Sundance::ObjectWithClassVerbosity< BasisFamilyBase > Sundance::BasisDOFTopologyBase Sundance::TensorBasisBase Sundance::BasisReferenceEvaluationBase Sundance::DefaultObjectWithVerbosity Sundance::ObjectWithVerbosityBase

List of all members.

Public Member Functions

 Nedelec (int spatialDim)
bool supportsCellTypePair (const CellType &maximalCellType, const CellType &cellType) const
 Inform caller as to whether a given cell type is supported.
void print (std::ostream &os) const
int order () const
int nReferenceDOFsWithoutFacets (const CellType &maximalCellType, const CellType &cellType) const
 return the number of nodes for this basis on the given cell type
void getReferenceDOFs (const CellType &maximalCellType, const CellType &cellType, Array< Array< Array< int > > > &dofs) const
 Get a description of the DOF numbering and distribution scheme for this basis function on the given cell type.
void refEval (const CellType &cellType, const Array< Point > &pts, const SpatialDerivSpecifier &deriv, Array< Array< Array< double > > > &result, int verbosity=0) const
 Evaluate the basis functions (or some mixed spatial derivative of the basis functions) for an array of points on the "reference cell" for a given cell type.

Private Member Functions

Handleable interface
void evalOnTriangle (int dir, const Point &pt, const SpatialDerivSpecifier &deriv, Array< double > &result) const
 evaluate on a triangle cell

Detailed Description

Lowest-order Nedelec basis.

Definition at line 43 of file SundanceNedelec.hpp.

Constructor & Destructor Documentation

Nedelec::Nedelec ( int  spatialDim)

Definition at line 45 of file SundanceNedelec.cpp.

Member Function Documentation

void Sundance::Nedelec::evalOnTriangle ( int  dir,
const Point &  pt,
const SpatialDerivSpecifier &  deriv,
Array< double > &  result 
) const [private]

evaluate on a triangle cell

void Nedelec::getReferenceDOFs ( const CellType &  maximalCellType,
const CellType &  cellType,
Array< Array< Array< int > > > &  dofs 
) const [virtual]

Get a description of the DOF numbering and distribution scheme for this basis function on the given cell type.

Parameters:
cellType[in] Specification of the cell topology
dofs[out] Array of dof numbering information, to be filled in during the call. On output, dofs.size()==dimension(cellType). See description of dofs below for more details.

The DOF description is returned in the nested array dofs, and is to be interpreted as follows: The outer dimension of the description array dofs.size() is cellDim, where cellDim is the spatial dimension of the cell. The DOFs attached to facets are stored in array entries dofs[s] where s=0...cellDim-1. Those associated with the cell body are stored in dofs[cellDim-1]. For cell dofs attached to facets, the dof facetDofIndex associated with the facet facetIndex of facet dimension facetDim is given by:

   dofs[facetDim][facetIndex][faceDofIndex]

For dofs attached to the cell body, the local DOF within the entire cell is given by dof is given by

   dofs[cellDim][0][dofIndex]

More specifically:

  • dof[facetDim].size() gives the number of facets of the facet dimension facetDim, where 0 <= facetDim <= cellDim

  • dof[facetDim][facetIndex].size() gives the number of degrees of freedom (DOFs) on the facet facetIndex with facet dimension facetDim, where 0 <= facetDim <= cellDim and 0 <= facetIndex < numFacets(cellType,facetDim).

For example, the Lagrange basis functions of order 0 through 3 on 2D triangles would have the following dof arrays:


   Order 0:

   { {}, {}, {{0}} }
   
   Order 1:

   { { {0}, {1}, {2} }, {}, {} }
    
   Order 2:

   { { {0}, {1}, {2} }, { {3}, {4}, {5} }, {} }
    
   Order 3:

   { { {0}, {1}, {2} }, { {3,4}, {5,6}, {7,8} }, {9} }

Above, we have used the ordering given in Hughes' textbook.

Implements Sundance::BasisDOFTopologyBase.

Definition at line 110 of file SundanceNedelec.cpp.

References Sundance::LineCell, Sundance::PointCell, Sundance::TetCell, and Sundance::TriangleCell.

int Nedelec::nReferenceDOFsWithoutFacets ( const CellType &  maximalCellType,
const CellType &  cellType 
) const [virtual]

return the number of nodes for this basis on the given cell type

Implements Sundance::BasisDOFTopologyBase.

Definition at line 89 of file SundanceNedelec.cpp.

References Sundance::LineCell, Sundance::PointCell, and Sundance::TriangleCell.

int Sundance::Nedelec::order ( ) const [inline, virtual]

Implements Sundance::BasisFamilyBase.

Definition at line 61 of file SundanceNedelec.hpp.

void Nedelec::print ( std::ostream &  os) const [virtual]

Implements Sundance::Printable.

Definition at line 84 of file SundanceNedelec.cpp.

void Nedelec::refEval ( const CellType &  cellType,
const Array< Point > &  pts,
const SpatialDerivSpecifier &  deriv,
Array< Array< Array< double > > > &  result,
int  verbosity = 0 
) const [virtual]

Evaluate the basis functions (or some mixed spatial derivative of the basis functions) for an array of points on the "reference cell" for a given cell type.

Parameters:
cellType[in] The type of cell on which the basis is currently being evaluated.
pts[in] Array of points on the reference cell (or master cell) where the basis functions are to be computed.
deriv[in] Specification of which differential operator is to be applied to the basis functions.
result[out] On output, gives a triply nested array which contain the basis functions (or the requested basis function derivatives) evaluated at the given points pts. The size of the outer array results is either zero or spatialDim, depending on whether this is a scalar or vector basis, respectively. The size of the next array level is equal to the number of evaluation points. Finally, the size of the innermost array level is equal to the number of DOFs visible from the given cell type. x * Specifically, 
           results[k][pointIndex][basisIndex]
gives the value of the spatial derivative of the $k$-th component of

\[\frac{\partial^{d_x+d_y+d_z}}{\partial x^{d_x} \partial y^{d_y} \partial z^{d_z}}\psi_i(x,y,z)\]

, where $d_x$ = deriv[0], $d_y$ = deriv[1] (in 2D or 3D) and $d_Z$ = deriv[2] (in 3D) at the point pointIndex (where 0 <= pointIndex < pts.size()) for the basis function $i$ = basisIndex (where 0 <= basisIndex < mapStructure.numBasisChunks()).

Implements Sundance::BasisReferenceEvaluationBase.

Definition at line 147 of file SundanceNedelec.cpp.

bool Nedelec::supportsCellTypePair ( const CellType &  maximalCellType,
const CellType &  cellType 
) const [virtual]

Inform caller as to whether a given cell type is supported.

Implements Sundance::BasisDOFTopologyBase.

Definition at line 49 of file SundanceNedelec.cpp.

References Sundance::LineCell, Sundance::PointCell, Sundance::TetCell, and Sundance::TriangleCell.

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