Geometry based on mapping by Lagrange basis functions

[CsatiZoltan]

This PR will implement an alternative volume mapping, see also #794.
Eventually, this contribution will provide the numerics for the mapping, i.e. points 1 and 3 in Sandro Elsweijer's comment. This PR is not concerned with the creation of a mesh reader. I plan to include

• several element types (T6, Q4, etc.) in 2D and 3D
• tests for all these element types
• examples/tutorials
• documentation
• potentially a method to generate the basis functions for arbitrary-order Lagrange finite elements

This is my first PR, so I do not yet know the structure of t8code. So please forgive me if the initial structuring of the code is inappropriate. Moreover, while I read the existing code and the contribution guidelines, I am beginner in C++.

---

All these boxes must be checked by the reviewers before merging the pull request:

As a reviewer please read through all the code lines and make sure that the code is fully understood, bug free, well-documented and well-structured.

General

• The reviewer executed the new code features at least once and checked the results manually

• The code follows the t8code coding guidelines

• New source/header files are properly added to the Makefiles

• The code is well documented

• All function declarations, structs/classes and their members have a proper doxygen documentation

• All new algorithms and data structures are sufficiently optimal in terms of memory and runtime (If this should be merged, but there is still potential for optimization, create a new issue)

Tests

• The code is covered in an existing or new test case using Google Test

Github action

• The code compiles without warning in debugging and release mode, with and without MPI (this should be executed automatically in a github action)

• All tests pass (in various configurations, this should be executed automatically in a github action)

  If the Pull request introduces code that is not covered by the github action (for example coupling with a new library):

  • Should this use case be added to the github action?
  • If not, does the specific use case compile and all tests pass (check manually)

Scripts and Wiki

• If a new directory with source-files is added, it must be covered by the script/find_all_source_files.scp to check the indentation of these files.
• If this PR introduces a new feature, it must be covered in an example/tutorial and a Wiki article.

Licence

• The author added a BSD statement to doc/ (or already has one)

[sandro-elsweijer]

Very nice implementation here. Maybe the files should get a more telling file name, like t8_geometry_lagrangian.cxx/hxx. Furthermore, we require a C wrapping for all our CPP concepts. For that, you can adapt the t8_geometry_linear.h and the according lines in the t8_geometry_linear.cxx

[sandro-elsweijer]

This looks very good! A batch computation would be nice, and I suggest some rigorous consting (I hope all those consts do not break the code), but the rest looks very mergeable

[sandro-elsweijer]

Hey Zoltan, apart from some minor things, this looks already merge-able!
However, a test would be nice.

[sandro-elsweijer]

I just realized, that we have to add you implementations into the Makefile as well! You can orient yourself by the other geometries.

[sandro-elsweijer]

Nice work! Proposed only minor improvements.

[sandro-elsweijer]

Just these two last things