Sundance::EdgeLocalizedBasis Class Reference

EdgeLocalizedBasis is a basis function defined only on edges. More...

Inheritance diagram for Sundance::EdgeLocalizedBasis:

Sundance::ScalarBasis Sundance::BasisFamilyBase Sundance::BasisFamilyBase Sundance::BasisReferenceEvaluationBase Sundance::TensorBasisBase Sundance::BasisDOFTopologyBase Sundance::ObjectWithClassVerbosity< BasisFamilyBase > Playa::Printable Playa::Handleable< BasisFamilyBase > Sundance::BasisReferenceEvaluationBase Sundance::TensorBasisBase Sundance::BasisDOFTopologyBase Sundance::ObjectWithClassVerbosity< BasisFamilyBase > Playa::Printable Playa::Handleable< BasisFamilyBase >

List of all members.

Public Member Functions

 EdgeLocalizedBasis ()
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
 abstract print function
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 evalOnLine (const Point &pt, const MultiIndex &deriv, Array< double > &result) const
 evaluate on a line cell
void evalOnTriangle (const Point &pt, const MultiIndex &deriv, Array< double > &result) const
 evaluate on a triangle cell
void evalOnTet (const Point &pt, const MultiIndex &deriv, Array< double > &result) const
 evaluate on a tet cell

Detailed Description

EdgeLocalizedBasis is a basis function defined only on edges.

Definition at line 43 of file SundanceEdgeLocalizedBasis.hpp.

Constructor & Destructor Documentation

EdgeLocalizedBasis::EdgeLocalizedBasis (  ) 

Definition at line 45 of file SundanceEdgeLocalizedBasis.cpp.

Member Function Documentation

void EdgeLocalizedBasis::evalOnLine ( const Point &  pt,
const MultiIndex &  deriv,
Array< double > &  result 
) const [private]

evaluate on a line cell

Definition at line 164 of file SundanceEdgeLocalizedBasis.cpp.

References Sundance::MultiIndex::firstOrderDirection(), Sundance::MultiIndex::order(), and Sundance::value.

Referenced by refEval().

void EdgeLocalizedBasis::evalOnTet ( const Point &  pt,
const MultiIndex &  deriv,
Array< double > &  result 
) const [private]

evaluate on a tet cell

Definition at line 245 of file SundanceEdgeLocalizedBasis.cpp.

Referenced by refEval().

void EdgeLocalizedBasis::evalOnTriangle ( const Point &  pt,
const MultiIndex &  deriv,
Array< double > &  result 
) const [private]

evaluate on a triangle cell

Definition at line 181 of file SundanceEdgeLocalizedBasis.cpp.

References Sundance::MultiIndex::firstOrderDirection(), Sundance::gradient(), Sundance::MultiIndex::order(), SUNDANCE_OUT, Sundance::value, Sundance::ADReal::value(), and Playa::ObjectWithVerbosity::verb().

Referenced by refEval().

void EdgeLocalizedBasis::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 90 of file SundanceEdgeLocalizedBasis.cpp.

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

int EdgeLocalizedBasis::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 76 of file SundanceEdgeLocalizedBasis.cpp.

References Sundance::LineCell.

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

Implements Sundance::BasisFamilyBase.

Definition at line 61 of file SundanceEdgeLocalizedBasis.hpp.

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

abstract print function

Implements Playa::Printable.

Definition at line 71 of file SundanceEdgeLocalizedBasis.cpp.

void EdgeLocalizedBasis::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 117 of file SundanceEdgeLocalizedBasis.cpp.

References Sundance::ScalarBasis::dim(), Sundance::dimension(), evalOnLine(), evalOnTet(), evalOnTriangle(), Sundance::SpatialDerivSpecifier::isIdentity(), Sundance::SpatialDerivSpecifier::isPartial(), and Sundance::SpatialDerivSpecifier::mi().

bool EdgeLocalizedBasis::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 48 of file SundanceEdgeLocalizedBasis.cpp.

References Sundance::BrickCell, Sundance::LineCell, Sundance::QuadCell, Sundance::TetCell, and Sundance::TriangleCell.

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