Arbitrary-Order SGH 3D solver (AO-SGH)

[steven-t-walton]

Description

Added high order discretization following closely Dobrev et al. 2012. The used GLL DoF distribution for kinematic space and GL DoF distribution for thermo. If either space is linear, uses one Neumann iteration to approximation mass matrix inverse and avoid dispersion error, otherwise it use a lumped mass if the space is not using polynomial degree 1. The reference element uses a sum factorization convention, allowing for fast computations of the action of an operator. Added high-order field visualization. Created several benchmark tests.

Requires further testing but good enough for a draft PR.
TO DO: Build and run on GPUs.

Type of change

Please select all relevant options

• New feature (non-breaking change which adds functionality)
• Bug fix (non-breaking change which fixes an issue)
• Formatting and/or style fixes
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• This change requires a documentation update

How Has This Been Tested?

The code has been run with openmp backend on cpu (Ubuntu laptop, gcc) and validated against the standard hydro benchmarks. This is enough for the draft PR. Will continue to test on gpu.

Checklist:

• My code follows the style guidelines of this project
• I have performed a self-review of my code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• My changes generate no new warnings
• The code builds from scratch with my new changes
• I have added tests that prove my fix is effective or that my feature works
• New and existing unit tests pass locally with my changes
• Any dependent changes have been merged and published in downstream modules