[FEM] Introduce higher accuracy quadrature rules

[th-skam]

For each Element, an option is added to use a higher-accuracy quadrature rule. The default behaviour of existing force fields is preserved. Lower-order rules are also included for completeness.

The purpose of this change is to enable more accurate error-norm computations in the V&V suite using the Method of Manufactured Solutions.

If the accuracy is insufficient, the integration introduces errors in the computed norms. This we observe either as the convergence rate approaching the expected one more slowly or as apparent superconvergence that counters the purpose of the test.

The degrees are:

Element	Up to degree	Default degree
Edge	3	1
Quad	3	2
Tri	2	1
Tetra	2	1
Hex	5	3

[with-all-tests]

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[alxbilger]

I would be curious to know how you use quadratureRule

[th-skam]

@alxbilger
It was used like so in my cases: 97581c5

[sofabot]

[ci-depends-on] detected during build #4.

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• Merge or close Bindings for quadrature data and element Jacobian SofaPython3#634
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  -DSOFAPYTHON3_GIT_REPOSITORY='https://github.com/sofa-framework/SofaPython3'
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[sofabot]

[ci-depends-on] detected during build #5.

To unlock the merge button, you must

• Merge or close Bindings for quadrature data and element Jacobian SofaPython3#634
  For this build, the following CMake flags will be set
  -DSOFAPYTHON3_GIT_REPOSITORY='https://github.com/sofa-framework/SofaPython3'
  -DSOFAPYTHON3_GIT_TAG='e094b25a72b3ebfa0bb993670a959c190ca7d642'

[alxbilger]

Could you just add the new quadrature points to the unit tests testSumWeights ? It's not enough, but there are not other tests for now...

[sofabot]

[ci-depends-on] detected during build #6.

To unlock the merge button, you must

• Merge or close Bindings for quadrature data and element Jacobian SofaPython3#634
  For this build, the following CMake flags will be set
  -DSOFAPYTHON3_GIT_REPOSITORY='https://github.com/sofa-framework/SofaPython3'
  -DSOFAPYTHON3_GIT_TAG='e094b25a72b3ebfa0bb993670a959c190ca7d642'

[alxbilger]

I think you can remove the ci-depends-on. It's actually the other PR that needs this one.

[th-skam]

Now that we added quadratic elements, I refactored the quadrature rules. Linear or quadratic, the integration is done over the same reference domain. The rules are now re-used, implemented in QuadratureRules.h. AI was used to help with std usage to have compile-time/runtime paths.

The literals were also substituted by std:: variants, wherever possible. This has triggered a unit test failure in ElementMass__test.

New rules can be added in the existing tables. There are two paths:

• Compile-time: using the function quadraturePoints<Degree>. It has a default value, and it is the one used by the existing FEM force fields
• Runtime: using quadratureRule and requesting a degree. I use this path for the source terms in [FEM] Add component for source term integration based on new FEM framework - constant source terms #6196

Each element has a default and minimum degree, so quadratic elements cannot use 1st order rules.
Will work on populating tests, either here or in subsequent PR.