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Add an exact solution for GetLocCoords of straight-edge quadrilateral element

Ankang Gao requested to merge gaoak/nektar:feature/QuadGetLocCoords into master

Issue/feature addressed

The mapping from the standard quadrilateral element to the straight-edge quadrilateral element is a quadratic function. This function can be solved analytically, instead of using the more expensive and less accurate Newton iteration.

Proposed solution

Screenshot_2023-12-09_at_13.21.54

Implementation

The above analytical solution is implemented in the function PreSolveStraightEdge and SolveStraightEdgeQuad

Tests

Previous tests are still working.

Suggested reviewers

Please suggest any people who would be appropriate to review your code.

Notes

Please add any other information that could be useful for reviewers.

Checklist

  • [ ] Functions and classes, or changes to them, are documented.
  • [ ] User guide/documentation is updated.
  • Changelog is updated.
  • [ ] Suitable tests added for new functionality.
  • Contributed code is correctly formatted. (See the contributing guidelines).
  • [ ] License added to any new files.
  • No extraneous files have been added (e.g. compiler output or test data files).
Edited by Jacques Xing

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