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PR 12116 #68

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PR 12116 #68

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Recreating Trilinos PR 12116 to study complexity.

…ilinos#12116)

* Intrepid2: add symmetric cubature rules for triangles and tetrahedra

These cubature rules are symmetric (invariant to orientation mappings) and have positive weights

* Intrepid2: modify integration tests to exercise new symmetric quadrature ruels

* Intrepid2: add capability to compute inverse of orientation maps

Inverse of orientation maps can be used to simplify the implementation of Lagrangian Interpolation

* Intrepid2: modify Largangian Interpolation implementation

We use inverse of orientation maps to simplify the implementation of Lagrangian Interpolation.
A major advantage is that now we provide an interpolation method that requires the
evaluation of the function on the reference dof nodes, which are the same in each cell,
instead of the "oriented" dof nodes that change from cell to cell.
This has the advantage of evaluating the basis functions only on the reference cell instead of on every cell.

* Intrepid2: Minor bug fixes and warnings removal

* Intrepid2: refactor of projections using new symmetric cubature rules

The use of symmetric cubature rules allow to require the evaluation of the
target function at points in the reference cell, which are the same in each cell,
instead of requesting the evaluation of the function at oriented quadrature points,
which can be different in different cells.

We refacor the projections so that the evaluation points are now stored in the ProjectionStruct
and can be accessed using the functions getAllEvalPoints() and getAllDerivEvalPoints.
And we change the implementation of the projection methods so that they use symmetric
quadrature rule and functions evaluated at the reference (non-oriented) points.

* Intrepid2: use new projection function in ProjectedGeometry

* Intrepid2: modify unit tests to use new projection and interpolation methods

Note: the results of some tests changed because we are using different quadrature rules.

* Intrepid2: Added projection tests for Wedge

* Panzer: modify implementation of MiniEM interpolation to use new Interpolation method

* Panzer: modify Dof Manager assembly tests to use new projection and interpolation functions
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