Discuss introduction of a more powerful math/tensor library

[amgebauer]

Description

I propose to include a new math library for our computations on the Gauss point. The library should implement tensors of arbitrary rank (also symmetric tensors) and the usual tensor products. Why? The implementation gets much closer to the equations on the paper (readability) and will be faster in implementing them. We also then don't need Voigt notations.

Features that I currently miss when using LINALG::Matrix for tensor quantities:

• Tensors instead of a Matrix
• Symmetric tensors, so that we don't have to mess with voigt notation (and convert forth and back all the time)
• tensor products (not just standard matrix multiplications and scalar products)
• fourth order tensors for the linearization

Possible Solution and Definition of Done

• Look for libraries out there. Candidates: The deal.ii tensor, Trilinos MiniTensor, fastor, KokkosKernels eigen
• Include it.
• Use it.

Related Issues and Merge Requests

• Related to https://gitlab.lrz.de/baci/baci/-/issues/363 https://gitlab.lrz.de/baci/baci/-/issues/746

Additional Information

Interested Parties

@4C-multiphysics/developers

[mrp089]

We're looking into Eigen to do that: SimVascular/svMultiPhysics#297
There is also a brief discussion of FEBio and deal.ii here: SimVascular/svMultiPhysics#177

[amgebauer]

Thank you for your input @mrp089. I added Eigen to the list of candidates.