Implementation of the default H(grad)-compatible Lagrange basis of arbitrary degree on Tetrahedron cell. More...
#include <Intrepid_HGRAD_TET_Cn_FEM.hpp>
Public Member Functions | |
| Basis_HGRAD_TET_Cn_FEM (const int n, const EPointType pointType) | |
| Constructor. | |
| void | getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const |
| Evaluation of a FEM basis on a reference Triangle cell. | |
| void | getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const ArrayScalar &cellVertices, const EOperator operatorType=OPERATOR_VALUE) const |
| FVD basis evaluation: invocation of this method throws an exception. | |
Private Member Functions | |
| virtual void | initializeTags () |
| Initializes tagToOrdinal_ and ordinalToTag_ lookup arrays. | |
Private Attributes | |
|
Basis_HGRAD_TET_Cn_FEM_ORTH < Scalar, FieldContainer < Scalar > > | Phis |
| The orthogonal basis on triangles, out of which the nodal basis is constructed. | |
| FieldContainer< Scalar > | V |
| The Vandermonde matrix with V_{ij} = phi_i(x_j), where x_j is the j_th point in the lattice. | |
| FieldContainer< Scalar > | Vinv |
| The inverse of V. The columns of Vinv express the Lagrange basis in terms of the orthogonal basis. | |
| FieldContainer< Scalar > | latticePts |
| stores the points at which degrees of freedom are located. | |
Detailed Description
template<class Scalar, class ArrayScalar>
class Intrepid::Basis_HGRAD_TET_Cn_FEM< Scalar, ArrayScalar >
Implementation of the default H(grad)-compatible Lagrange basis of arbitrary degree on Tetrahedron cell.
Implements Lagrangian basis of degree n on the reference Tetrahedron cell. The basis has cardinality (n+1)(n+2)(n+3)/6 and spans a COMPLETE polynomial space of degree n. Nodal basis functions are dual to a unisolvent set of degrees-of-freedom (DoF) defined at a lattice of order n (see PointTools). In particular, the degrees of freedom are point evaluation at
- The vertices
- (n-1) points on each edge of the tetrahedron
- max((n-1)(n-2)/2,0) points on each face of the tetrahedron
- max((n-1)(n-2)(n-3)/6,0) points in the interior of the tetrahedron.
The distribution of these points is specified by the pointType argument to the class constructor. Currently, either equispaced lattice points or Warburton's warp-blend points are available.
The dof are enumerated according to the ordering on the lattice (see PointTools). In particular, dof number 0 is at the vertex (0,0,0). The dof increase along the lattice with points along the lines of constant x adjacent in the enumeration.
Definition at line 88 of file Intrepid_HGRAD_TET_Cn_FEM.hpp.
Member Function Documentation
| void Intrepid::Basis_HGRAD_TET_Cn_FEM< Scalar, ArrayScalar >::getValues | ( | ArrayScalar & | outputValues, |
| const ArrayScalar & | inputPoints, | ||
| const EOperator | operatorType | ||
| ) | const [virtual] |
Evaluation of a FEM basis on a reference Triangle cell.
Returns values of operatorType acting on FEM basis functions for a set of points in the reference Triangle cell. For rank and dimensions of I/O array arguments see Section MD array template arguments for basis methods .
- Parameters:
-
outputValues [out] - variable rank array with the basis values inputPoints [in] - rank-2 array (P,D) with the evaluation points operatorType [in] - the operator acting on the basis functions
Implements Intrepid::Basis< Scalar, ArrayScalar >.
Definition at line 257 of file Intrepid_HGRAD_TET_Cn_FEMDef.hpp.
Referenced by main().
The documentation for this class was generated from the following files:
- /usr/src/RPM/BUILD/trilinos-11.12.1/packages/intrepid/src/Discretization/Basis/Intrepid_HGRAD_TET_Cn_FEM.hpp
- /usr/src/RPM/BUILD/trilinos-11.12.1/packages/intrepid/src/Discretization/Basis/Intrepid_HGRAD_TET_Cn_FEMDef.hpp
