perf(ghost): read the boundary geometry at its level in the outer ghost update

[gouarin]

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Description

Half to 60 % of ghost update (advection 2D and 3D, scalar Burgers 2D) is the filling of the outer ghosts by the boundary conditions, and 85 to 90 % of that phase is pure set algebra visiting 20 to 40 rows per interval emitted. Two causes, both in the way the expressions are written:

• the domain, the corners and the B.C. regions are stored at max_level and coarsened on the fly with self(x).on(level), whose traverser materialises 2^(max_level - level) fine rows per coarse row;
• difference(cells, translate(domain, -d)) visits every row of cells even when the boundary in direction d lies on a single row.

The geometry that depends on the domain only is now built once per domain at every level and inherited by the meshes constructed from a reference mesh (level_pyramid.hpp):

• mesh.corner(direction, level): corner pyramids. This also stops construct_corners from recomputing the domain corners at every mesh construction (2.1 s of a 17.7 s 3D run);
• mesh.boundary_inner_layer(level, d) = domain \ translate(domain, -d) and mesh.boundary_outer_layer(level, d, k) = translate(domain, k d) \ translate(domain, (k - 1) d);
• bc.region(d, level): the B.C. regions at every level.

The outer ghost expressions read those sets at their level and intersect with the thin layers instead of subtracting the domain: domain_boundary is intersection(cells, inner layer); project_bc intersects the translated union with the outer layer (the union lies inside the domain, so the sets are the same); predict_bc, on a box domain, predicts each layer straight from the expression with the order-0 prediction kernel per interval instead of materialising a level cell array and copying cell by cell. The non-box paths keep their former expressions.

The first commit adds the measurement build used to find this (-DSAMURAI_MEASURE_SET_ALGEBRA=ON, off by default, expands to nothing otherwise): per-phase timers in update_ghost_mr and, per apply(), the pure set algebra time, the rows visited, the intervals emitted, the row blocks and the empty row segments. It can be reviewed or dropped independently of the second commit.

Measurements

Sandbox Linux aarch64, gcc 15, Release, 3 runs, median, --timers, --nfiles 1:

	advection 2D (levels 4-10)	scalar Burgers 2D (levels 4-10)	advection 3D (levels 4-8)
ghost update (adaptation)	0.430 s -> 0.241 s (x1.78)	2.583 s -> 1.819 s (x1.42)	4.225 s -> 2.219 s (x1.90)
ghost update (time loop)	0.213 s -> 0.121 s (x1.76)	1.281 s -> 0.895 s (x1.43)	2.047 s -> 1.064 s (x1.92)
mesh construction	0.243 s -> 0.227 s	1.548 s -> 1.486 s	3.951 s -> 1.889 s (x2.09)
total runtime	2.302 s -> 1.991 s (x1.16)	12.427 s -> 11.205 s (x1.11)	17.710 s -> 12.651 s (x1.40)

bench_set (3 repetitions, medians): no entry moves by more than 2 %, the codegen canary BM_RefineFootprint_adapted<3> is unchanged; subset/ is not touched. Not yet measured with clang on macOS nor with MPI.

Related issue

None.

How has this been tested?

• h5diff on the 16 HDF5 files written by finite-volume-advection-2d (both prediction stencils), finite-volume-scalar-burgers-2d and finite-volume-advection-3d: bit-identical to main.
• New tests/test_boundary_geometry.cpp (2D and 3D, adapted mesh whose refinement reaches the boundary and the corners, levels 2 to 6): every precomputed set equals its .on(level) definition cell by cell, every rewritten expression equals its former form, and the predict_bc layers are disjoint.
• test_samurai_lib: 442 tests pass (440 existing + 2 new).
• All targets (demos, tests, benchmarks) compile.

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[codacy-production]

Up to standards ✅

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🟢 Metrics 17 complexity · 0 duplication

Metric	Results
Complexity	17
Duplication	0

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