Multigrid solver (V, W, F and K cycle) and example

[yhmtsai]

This PR adds the Multigrid solver with different cycle scheme (V, W, F, and K) and example

The current usage will be:

multigrid_factory =
            Solver::build()
                .with_max_levels(2u)
                .with_coarsest_solver(LinOpFactory)
                .with_pre_smoother(LinOpFactory, LinOpFactory2, ...)
                .with_post_smoother(LinOpFactory)
                .with_mg_level(MultigridLevelFactory1, MultigridLevelFactory2, ...)
                .on(exec);

.with_mg_level can allow several MultigridLevel factories. and .with_mg_level_index can be custom selector.
default selector 1. always return 0 if mg_level.size == 1; 2. return the level as index if mg_level.size > 1;

TODO:

• Merge Amgx parallel graph match reference and fill_seq_array #528 (amgxpgm core/reference)
• Merge AmgxPgm cuda/hip/omp implementation and matrix/array utils #695 (amgxpgm device)
• Add missing relaxation factor
• Might use one big workspace not multiple ones. keep separate workspace to handle different type easily in the future
• Rebase to last state
• clean the some debug message and add the missing documentation.

[codecov]

Codecov Report

Merging #542 (cb08a25) into develop (2bf7411) will decrease coverage by 0.00%.
The diff coverage is 93.62%.

@@             Coverage Diff             @@
##           develop     #542      +/-   ##
===========================================
- Coverage    94.30%   94.29%   -0.01%     
===========================================
  Files          416      423       +7     
  Lines        33063    34660    +1597     
===========================================
+ Hits         31179    32683    +1504     
- Misses        1884     1977      +93     

Impacted Files	Coverage Δ
core/device_hooks/common_kernels.inc.cpp	0.00% <0.00%> (ø)
include/ginkgo/core/base/composition.hpp	93.93% <ø> (ø)
omp/components/fill_array.cpp	100.00% <ø> (ø)
reference/components/fill_array.cpp	100.00% <ø> (ø)
core/test/solver/ir.cpp	96.05% <84.61%> (-2.37%)	⬇️
core/test/solver/multigrid.cpp	89.52% <89.52%> (ø)
core/solver/multigrid.cpp	93.37% <93.37%> (ø)
reference/test/multigrid/amgx_pgm_kernels.cpp	97.67% <93.75%> (-0.41%)	⬇️
reference/test/solver/multigrid_kernels.cpp	95.30% <95.30%> (ø)
include/ginkgo/core/solver/multigrid.hpp	98.75% <98.75%> (ø)
... and 18 more

---

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[hartwiganzt]

I imagine it being very difficult to accumulate all temorary data in a single workspace as the size is very hard to determine upfront. Correct me if I am wrong.

[yhmtsai]

@hartwiganzt
I create r, g, e dense matrix for each level in the beginning of apply, so I can combine all r into one workspace. like R = [r0; r1; r2] (each r is a row-major dense) such that it keeps the same stride as split case. By doing so, using only one kernel not multiple kernels to initialize the workspace reduces the overhead but might exceed the limit of size_type.

[sonarcloud]

Kudos, SonarCloud Quality Gate passed!

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140 Code Smells

70.7% Coverage
7.0% Duplication

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[sonarcloud]

Kudos, SonarCloud Quality Gate passed!   

0 Bugs
0 Vulnerabilities
0 Security Hotspots
79 Code Smells

64.1% Coverage
6.4% Duplication