Computes the Jacobian matrix DF of the reference-to-physical frame map F. More...
#include <Intrepid_CellTools.hpp>
Detailed Description
template<class Scalar>
template<class ArrayJac, class ArrayPoint, class ArrayCell, bool typecheck>
struct Intrepid::CellTools< Scalar >::setJacobianTempSpec< ArrayJac, ArrayPoint, ArrayCell, typecheck >
Computes the Jacobian matrix DF of the reference-to-physical frame map F.
There are three use cases:
- Computes Jacobians
of the reference-to-physical map for a specified physical cell 
from a cell workset on a single set of reference points stored in a rank-2 (P,D) array; - Computes Jacobians of the reference-to-physical map for all physical cells in a cell workset on a single set of reference points stored in a rank-2 (P,D) array;
- Computes Jacobians of the reference-to-physical map for all physical cells in a cell workset on multiple reference point sets having the same number of points, indexed by cell ordinal, and stored in a rank-3 (C,P,D) array;
For a single point set in a rank-2 array (P,D) and whichCell set to a valid cell ordinal relative to cellWorkset returns a rank-3 (P,D,D) array such that
![\[ \mbox{jacobian}(p,i,j) = [DF_{c}(\mbox{points}(p))]_{ij} \quad \mbox{for $0\le c < C$ - fixed} \]](form_37.png)
For a single point set in a rank-2 array (P,D) and whichCell=-1 (default value) returns a rank-4 (C,P,D,D) array such that
![\[ \mbox{jacobian}(c,p,i,j) = [DF_{c}(\mbox{points}(p))]_{ij} \quad c=0,\ldots, C \]](form_38.png)
For multiple sets of reference points in a rank-3 (C,P,D) array returns rank-4 (C,P,D,D) array such that
![\[ \mbox{jacobian}(c,p,i,j) = [DF_{c}(\mbox{points}(c,p))]_{ij} \quad c=0,\ldots, C \]](form_39.png)
This setting requires the default value whichCell=-1.
Requires cell topology with a reference cell. See Section Jacobian of the reference-to-physical cell mapping for definition of the Jacobian.
The default whichCell = -1 forces computation of all cell Jacobians and requiers rank-4 output array. Computation of single cell Jacobians is forced by selecting a valid cell ordinal whichCell and requires rank-3 output array.
- Warning
- The points are not required to be in the reference cell associated with the specified cell topology. CellTools provides several inclusion tests methods to check whether or not the points are inside a reference cell.
- Parameters
-
jacobian [out] - rank-4/3 array with dimensions (C,P,D,D)/(P,D,D) with the Jacobians points [in] - rank-2/3 array with dimensions (P,D)/(C,P,D) with the evaluation points cellWorkset [in] - rank-3 array with dimensions (C,N,D) with the nodes of the cell workset cellTopo [in] - cell topology of the cells stored in cellWorksetwhichCell [in] - cell ordinal (for single cell Jacobian computation); default is -1
Definition at line 350 of file Intrepid_CellTools.hpp.
The documentation for this struct was generated from the following file:
- http://docs.trilinos.org/r13.0/packages/intrepid/src/Cell/Intrepid_CellTools.hpp
