[SofaSparseSolver] Introduce FillReducingOrdering

[alxbilger]

A new DataEngine is introduced: FillReducingOrdering

A DataEngine to reorder the degrees of freedom in a mesh in order to reduce fill-in in sparse matrix factorization.

In other terms, the algorithm minimizes the number of non-zeros entries in the factorization of the sparse matrix of a FEM problem by reordering the degrees of freedom.

The implementation is based on METIS.

Note: some of the direct linear solvers embed such a reordering internally (e.g. SparseLDLSolver), but not all of them (e.g SparseLUSolver, SparseCholeskySolver etc).

An example is also introduced (examples/Components/engine/FillReducingOrdering.scn).
Here is the comparison of the two system matrices:

Initial matrix:

Reordered matrix:

It improves a lot the performances when the linear solver does not embed a fill-in reducing reordering. This is the case of the SparseLUSolver in the example scene.
Rough framerate without reordering: 2.5 FPS
Rough framerate with reordering: 25 FPS

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Reviewers will merge this pull-request only if

• it builds with SUCCESS for all platforms on the CI.
• it does not generate new warnings.
• it does not generate new unit test failures.
• it does not generate new scene test failures.
• it does not break API compatibility.
• it is more than 1 week old (or has fast-merge label).

[alxbilger]

[ci-build][with-all-tests]

[fredroy]

By curiosity, do you think using mt-metis (metis with openmp in a nutshell) could be useful ?
I am quite not sure because I suppose the speedup would come for a mesh with a huge number of nodes but still... 🧐

[alxbilger]

By curiosity, do you think using mt-metis (metis with openmp in a nutshell) could be useful ? I am quite not sure because I suppose the speedup would come for a mesh with a huge number of nodes but still... 🧐

@fredroy I don't think it's a priority. The reordering is computed only at initialization. And you can always export your new mesh for later use.

[guparan]

LGTM but the new example FillReducingOrdering.scn crashes (timeout) on all platforms 😢

[alxbilger]

[ci-build][with-all-tests]