Public Member Functions
Sundance::Lagrange Class Reference

Lagrange basis. More...

Inheritance diagram for Sundance::Lagrange:
Sundance::ScalarBasis Sundance::BasisFamilyBase Sundance::BasisFamilyBase Sundance::BasisReferenceEvaluationBase Sundance::TensorBasisBase Sundance::BasisDOFTopologyBase Sundance::ObjectWithClassVerbosity< BasisFamilyBase > Sundance::Printable Sundance::Handleable< BasisFamilyBase > Sundance::BasisReferenceEvaluationBase Sundance::TensorBasisBase Sundance::BasisDOFTopologyBase Sundance::ObjectWithClassVerbosity< BasisFamilyBase > Sundance::Printable Sundance::Handleable< BasisFamilyBase >

List of all members.

Public Member Functions

 Lagrange (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
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.
void getConstrainsForHNDoF (const int indexInParent, const int maxCellDim, const int maxNrChild, const int facetDim, const int facetIndex, const int nodeIndex, Array< int > &localDoFs, Array< int > &parentFacetDim, Array< int > &parentFacetIndex, Array< int > &parentFacetNode, Array< double > &coefs)
 constraints for hanging DoFs

Handleable interface

int order_
bool doFInfromationCalculated_
Array< int > facetD_
 For each DoF the dimension of the element which is the DoF on.
Array< int > facetI_
 For each DoF the facet index of the element.
Array< int > facetN_
 For each DoF the facet index of the element.
std::string description () const
static Array< int > makeRange (int low, int high)
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 evalOnquad (const Point &pt, const MultiIndex &deriv, Array< double > &result) const
 evaluate on a quad cell
void evalOnTet (const Point &pt, const MultiIndex &deriv, Array< double > &result) const
 evaluate on a tet cell
void evalOnBrick (const Point &pt, const MultiIndex &deriv, Array< double > &result) const
 evaluate on a tet cell
void returnDoFPositionOnRef (const int maxCellDim, const int facetDim, const int facetIndex, const int nodeIndex, Point &pos) const
 get the exact position one DoF on the Ref Element this is needed for the treatment of hanging nodes
void getDoFsOrdered (const CellType maxCellDim, int nrDoF, Array< int > &facetD, Array< int > &facetI, Array< int > &facetN)
 This method calls the "getReferenceDOFs" method and then for each DoF extracts the facet dimension, facet index and node in 3 different array
This method could be used for general purpose for other basis, where HN is possible.

Detailed Description

Lagrange basis.

Definition at line 43 of file SundanceLagrange.hpp.

Constructor & Destructor Documentation

Lagrange::Lagrange ( int  order)

Definition at line 45 of file SundanceLagrange.cpp.

Member Function Documentation

std::string Sundance::Lagrange::description ( ) const [inline]

Definition at line 102 of file SundanceLagrange.hpp.

References order(), and Sundance::toString().

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

evaluate on a tet cell

Definition at line 628 of file SundanceLagrange.cpp.

References Sundance::MultiIndex::firstOrderDirection(), Sundance::MultiIndex::order(), order_, SUNDANCE_ERROR, SUNDANCE_ERROR7, and Sundance::value.

Referenced by refEval().

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

evaluate on a line cell

Definition at line 360 of file SundanceLagrange.cpp.

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

Referenced by refEval().

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

evaluate on a quad cell

Definition at line 506 of file SundanceLagrange.cpp.

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

Referenced by refEval().

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

evaluate on a tet cell

Definition at line 571 of file SundanceLagrange.cpp.

References Sundance::MultiIndex::firstOrderDirection(), Sundance::MultiIndex::order(), order_, SUNDANCE_ERROR, SUNDANCE_ERROR7, and Sundance::value.

Referenced by refEval().

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

evaluate on a triangle cell

Definition at line 428 of file SundanceLagrange.cpp.

References Sundance::MultiIndex::firstOrderDirection(), Sundance::gradient(), Sundance::MultiIndex::order(), order_, SUNDANCE_ERROR, SUNDANCE_ERROR7, SUNDANCE_OUT, Sundance::value, Sundance::ADReal::value(), and Sundance::DefaultObjectWithVerbosity::verb().

Referenced by refEval().

void Lagrange::getConstrainsForHNDoF ( const int  indexInParent,
const int  maxCellDim,
const int  maxNrChild,
const int  facetDim,
const int  facetIndex,
const int  nodeIndex,
Array< int > &  localDoFs,
Array< int > &  parentFacetDim,
Array< int > &  parentFacetIndex,
Array< int > &  parentFacetNode,
Array< double > &  coefs 
) [virtual]

constraints for hanging DoFs

Reimplemented from Sundance::BasisReferenceEvaluationBase.

Definition at line 932 of file SundanceLagrange.cpp.

References Sundance::BrickCell, doFInfromationCalculated_, facetD_, facetI_, facetN_, getDoFsOrdered(), Sundance::QuadCell, refEval(), returnDoFPositionOnRef(), SUNDANCE_OUT, and Sundance::DefaultObjectWithVerbosity::verb().

void Lagrange::getDoFsOrdered ( const CellType  maxCellDim,
int  nrDoF,
Array< int > &  facetD,
Array< int > &  facetI,
Array< int > &  facetN 
) [private]

This method calls the "getReferenceDOFs" method and then for each DoF extracts the facet dimension, facet index and node in 3 different array
This method could be used for general purpose for other basis, where HN is possible.

Parameters:
maxCellDim[in]
nrDoF[in] nr of DoF for this element
facetD[out]
facetI[out]
facetN[out]

Definition at line 1187 of file SundanceLagrange.cpp.

References getReferenceDOFs(), SUNDANCE_OUT, and Sundance::DefaultObjectWithVerbosity::verb().

Referenced by getConstrainsForHNDoF().

void Lagrange::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 168 of file SundanceLagrange.cpp.

References Sundance::BrickCell, Sundance::ScalarBasis::dim(), Sundance::dimension(), Sundance::LineCell, makeRange(), Sundance::numFacets(), order(), order_, Sundance::PointCell, Sundance::QuadCell, Sundance::TetCell, and Sundance::TriangleCell.

Referenced by getDoFsOrdered().

Array< int > Lagrange::makeRange ( int  low,
int  high 
) [static, private]

Definition at line 291 of file SundanceLagrange.cpp.

Referenced by getReferenceDOFs().

int Lagrange::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 120 of file SundanceLagrange.cpp.

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

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

Implements Sundance::BasisFamilyBase.

Definition at line 61 of file SundanceLagrange.hpp.

References order_.

Referenced by description(), evalOnLine(), Sundance::ExprFieldWrapper::ExprFieldWrapper(), getReferenceDOFs(), Sundance::DOFMapBuilder::hasCellBasis(), Sundance::DOFMapBuilder::hasNodalBasis(), and returnDoFPositionOnRef().

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

Implements Sundance::Printable.

Definition at line 115 of file SundanceLagrange.cpp.

References order_.

void Lagrange::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 300 of file SundanceLagrange.cpp.

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

Referenced by getConstrainsForHNDoF().

void Lagrange::returnDoFPositionOnRef ( const int  maxCellDim,
const int  facetDim,
const int  facetIndex,
const int  nodeIndex,
Point &  pos 
) const [private]

get the exact position one DoF on the Ref Element this is needed for the treatment of hanging nodes

Parameters:
maxCellDim[in] the MaxCell dim of this element
facetDim[in] the facet dim which the DoF is on
facetIndex[in] the facet index which the DoF is on
nodeIndex[in] the node index of the DoF
pos[out] the position of the DoF

Definition at line 1106 of file SundanceLagrange.cpp.

References order().

Referenced by getConstrainsForHNDoF().

bool Lagrange::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 53 of file SundanceLagrange.cpp.

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

Member Data Documentation

bool Sundance::Lagrange::doFInfromationCalculated_ [private]

Definition at line 166 of file SundanceLagrange.hpp.

Referenced by getConstrainsForHNDoF().

Array<int> Sundance::Lagrange::facetD_ [private]

For each DoF the dimension of the element which is the DoF on.

Definition at line 169 of file SundanceLagrange.hpp.

Referenced by getConstrainsForHNDoF().

Array<int> Sundance::Lagrange::facetI_ [private]

For each DoF the facet index of the element.

Definition at line 172 of file SundanceLagrange.hpp.

Referenced by getConstrainsForHNDoF().

Array<int> Sundance::Lagrange::facetN_ [private]

For each DoF the facet index of the element.

Definition at line 175 of file SundanceLagrange.hpp.

Referenced by getConstrainsForHNDoF().

int Sundance::Lagrange::order_ [private]

Definition at line 106 of file SundanceLagrange.hpp.

Referenced by evalOnBrick(), evalOnLine(), evalOnquad(), evalOnTet(), evalOnTriangle(), getReferenceDOFs(), nReferenceDOFsWithoutFacets(), order(), and print().

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