Backware Euler with vectorizable matrix types

[mattldawson]

Adapts the Backward Euler solver to work with vectorizable matrices.

closes #500

Also:

• moves physical constants and labels into dedicated namespaces
• adapts analytical tests to solve for multiple grid cells
• results in a net increase of only one line of code!

[K20shores]

Nice! Only a few questions, but nothing that would hold this up

[sjsprecious]

Thanks @mattldawson for working on this giant PR and this functionality looks great. Just have one question as listed below.

[boulderdaze]

Looks good! I don't see anything other than what others have commented on. I left one comment but it shouldn't hold this PR getting merged.

[sjsprecious]

Running on Derecho with NVHPC, I got the following failed tests:

         34 - analytical_rosenbrock_integration (Failed)
         35 - analytical_backward_euler (Failed)
         38 - cuda_analytical_rosenbrock_integration (Subprocess aborted)

Looking at the output log, the difference is slightly above the given tolerance. I wonder whether we can add a check to the relative error (like https://github.com/NCAR/micm/blob/main/test/unit/solver/test_rosenbrock.cpp#L138-L139) and pass the test if the relative error is small enough (say < 1.e-14?).

[mwaxmonsky]

Looks great @mattldawson! Just one quick recommendation but nothing worth holding things up.

[mwaxmonsky]

We might want to add some checks on the non-diagonal to make sure we are only incrementing the expected indices.

[mattldawson]

added!

[mattldawson]

Running on Derecho with NVHPC, I got the following failed tests:

         34 - analytical_rosenbrock_integration (Failed)
         35 - analytical_backward_euler (Failed)
         38 - cuda_analytical_rosenbrock_integration (Subprocess aborted)

Looking at the output log, the difference is slightly above the given tolerance. I wonder whether we can add a check to the relative error (like https://github.com/NCAR/micm/blob/main/test/unit/solver/test_rosenbrock.cpp#L138-L139) and pass the test if the relative error is small enough (say < 1.e-14?).

I modified the analytical policy tests to include a relative error check and the two CPU tests pass now. Still waiting on the CUDA analytical test to run.

[mattldawson]

Running on Derecho with NVHPC, I got the following failed tests:

         34 - analytical_rosenbrock_integration (Failed)
         35 - analytical_backward_euler (Failed)
         38 - cuda_analytical_rosenbrock_integration (Subprocess aborted)

Looking at the output log, the difference is slightly above the given tolerance. I wonder whether we can add a check to the relative error (like https://github.com/NCAR/micm/blob/main/test/unit/solver/test_rosenbrock.cpp#L138-L139) and pass the test if the relative error is small enough (say < 1.e-14?).

I modified the analytical policy tests to include a relative error check and the two CPU tests pass now. Still waiting on the CUDA analytical test to run.

The CUDA tests now pass with some slightly adjusted tolerances.

[sjsprecious]

Thanks @mattldawson for working on this and addressing all the comments. I could confirm that all the tests passed on Derecho's A100 GPU.