Index-based mlebabeclap_adotx_centroid kernel

[ankithadas]

Summary

Rewrites mlebabeclap_adotx_centroid (2D and 3D) from a Box-based kernel that loops
internally (amrex::Loop(box, ncomp, ...)) into a per-cell (i,j,k,n) kernel, and
replaces its eleven separate EB Array4 arguments (flag, vfrc, apx/apy/apz,
fcx/fcy/fcz, ccent, ba, bcent) with the existing EBData view.

MLEBABecLap::Fapply now calls it through AMREX_HOST_DEVICE_PARALLEL_FOR_4D and gets
all EB geometry from factory->getEBData(mfi), which lets the getVolFrac() /
getAreaFrac() / getFaceCent() / getBndryArea() / getBndryCent() / getCentroid()
lookups at the top of Fapply be dropped entirely.

The arithmetic inside the kernel is untouched: the loop wrapper is removed and the body is
only re-indented, and the EB arrays are re-bound to identically named local references
(auto const& ccent = ebdata.get<EBData_t::centroid>(); etc.), so the expressions are
character for character the same. Results are bitwise unchanged.

Additional background

This is part of the ongoing split of the stale WIP #4922 ("GPU specific kernels for
MLEBABecLap"), as requested there; it supersedes the mlebabeclap_adotx_centroid part of
#4922. The templating on T that #4922 also introduced has been dropped, per the review
comment on that PR.

This PR is stacked on top of the mlebabeclap_adotx PR (branch
ankithadas:MLEBABecLap-Adotx-Index) because both edit the same block of
MLEBABecLap::Fapply; please merge that one first. The diff shown here against
development therefore contains that commit as well.

Testing (all commands run from the repo root unless noted):

• cmake -S . -B build-split -DAMReX_SPACEDIM=3 -DAMReX_EB=ON -DAMReX_LINEAR_SOLVERS_EM=OFF -DAMReX_ENABLE_TESTS=ON -DAMReX_TEST_TYPE=Small -DAMReX_MPI=ON -DCMAKE_BUILD_TYPE=Release
  then cmake --build build-split -j8 and ctest --test-dir build-split --output-on-failure
  → builds clean, 9/9 tests pass. A 2D library build
  (-DAMReX_SPACEDIM=2 -DAMReX_EB=ON) also builds clean.

• Tests/LinearSolvers/LeastSquares is the test that actually exercises this kernel: it
  calls MLEBABecLap::setPhiOnCentroid() and then MLMG::apply(). Built with
  make -j8 COMP=llvm USE_MPI=FALSE DIM=2 and DIM=3, and run on
  inputs.2d.base, inputs.2d.askew-x, inputs.2d.fullyrotated,
  inputs.2d.trianglewave, inputs.3d.poiseuille.askew-all and
  inputs.3d.poiseuille.aligned.xy-x. The resulting plotfiles are byte for byte
  identical to those produced by development (diff -r over all six).

• Tests/LinearSolvers/CellEB, make -j8 COMP=llvm USE_MPI=FALSE DIM=3 and DIM=2,
  seven configurations (sphere, sphere + eb_is_dirichlet=1, rotated_box,
  two_spheres, flower, two-level sphere, periodic sphere; n_cell=64,
  verbose=2): MLMG/BiCGStab residual histories and final residual norms are bitwise
  identical to development.

• CUDA build on an NVIDIA RTX A5000 (CUDA 13.2, gcc 11.4):
  Tests/LinearSolvers/CellEB, make -j8 COMP=gnu USE_MPI=FALSE USE_CUDA=TRUE CUDA_ARCH=86 DIM=3.
  MLMG iteration counts are identical to development (9, 12, 11, 3, 11, 28, 11); the
  residual values differ only at the level of the run-to-run nondeterminism of the
  unmodified binary (GPU reductions are not bit-reproducible).

• The same CellEB matrix was re-run on Linux/gcc 11.4 (make -j8 COMP=gnu USE_MPI=FALSE,
  DIM=3 and DIM=2) against a development build in a sibling worktree: residual
  histories again bitwise identical in both dimensions.

Performance

Neither timing changed measurably; this PR is a refactor, not an optimisation.

CPU, Tests/LinearSolvers/CellEB main3d.gnu.TEST.ex
(make -j8 COMP=gnu USE_MPI=FALSE DIM=3, gcc 11.4, single rank),
inputs n_cell=128 eb2.geom_type=sphere eb_is_dirichlet=1 verbose=1.
All binaries were built first and then timed interleaved in the same session
(3 reps each) on a shared machine, so the absolute numbers are inflated but the
comparison is fair. Best of 3, MLMG Timers: Solve [s]:

grids	development	this PR
max_grid_size=32	4.284	4.325
max_grid_size=64	4.534	4.553

GPU (NVIDIA RTX A5000, CUDA 13.2,
make -j8 COMP=gnu USE_MPI=FALSE USE_CUDA=TRUE CUDA_ARCH=86 DIM=3), same test at
n_cell=256, again built up front and timed interleaved, best of 3:

grids	development	this PR
max_grid_size=32 (512 boxes)	1.085	1.083
max_grid_size=64 (64 boxes)	0.834	0.824

MLMG converged in the same number of iterations in every one of these runs.

Checklist

The proposed changes:

• fix a bug or incorrect behavior in AMReX
• add new capabilities to AMReX
• changes answers in the test suite to more than roundoff level
• are likely to significantly affect the results of downstream AMReX users
• include documentation in the code and/or rst files, if appropriate

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