Sundance::Bubble Class Reference

Bubble function for use in error estimation. More...

Inheritance diagram for Sundance::Bubble:

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

 Bubble (int order)
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.

Handleable interface

int order_
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

Bubble function for use in error estimation.

Definition at line 43 of file SundanceBubble.hpp.

Constructor & Destructor Documentation

Sundance::Bubble::Bubble ( int  order  )  [inline]

Definition at line 47 of file SundanceBubble.hpp.

Member Function Documentation

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

evaluate on a line cell

Definition at line 214 of file SundanceBubble.cpp.

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

Referenced by refEval().

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

evaluate on a tet cell

Definition at line 281 of file SundanceBubble.cpp.

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

Referenced by refEval().

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

evaluate on a triangle cell

Definition at line 238 of file SundanceBubble.cpp.

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

Referenced by refEval().

void Bubble::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 103 of file SundanceBubble.cpp.

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

int Bubble::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 94 of file SundanceBubble.cpp.

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

Implements Sundance::BasisFamilyBase.

Definition at line 61 of file SundanceBubble.hpp.

References order_.

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

abstract print function

Implements Playa::Printable.

Definition at line 89 of file SundanceBubble.cpp.

References order_.

void Bubble::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 166 of file SundanceBubble.cpp.

References evalOnLine(), evalOnTet(), evalOnTriangle(), Sundance::SpatialDerivSpecifier::isIdentity(), Sundance::SpatialDerivSpecifier::isPartial(), Sundance::LineCell, Sundance::SpatialDerivSpecifier::mi(), Sundance::PointCell, Sundance::TetCell, and Sundance::TriangleCell.

bool Bubble::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 47 of file SundanceBubble.cpp.

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

Member Data Documentation

int Sundance::Bubble::order_ [private]

Definition at line 105 of file SundanceBubble.hpp.

Referenced by evalOnLine(), evalOnTet(), evalOnTriangle(), order(), and print().

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