[SofaCUDA] ElementFEMForceField: Generic CUDA implementation

[fredroy]

Based on

• [FEM.Elastic] FEMForcefield: getExecutionPolicy did not use the provided data #6066
• [FEM.Elastic] Cache stiffness matrices before computations #6069
• [FEM.Elastic] Fix includes #6070

Implementation of the #5882 for SofaCUDA.
Claude did the heavy-lifting job :

Add CUDA-accelerated implementations of ElementLinearSmallStrainFEMForceField and 
ElementCorotationalFEMForceField for both float and double precision (CudaVec3f/CudaVec3d). Uses a two-kernel   
approach (per-element compute + per-vertex gather) with SoA memory layout for coalesced GPU access. The 
corotational version supports full GPU-side rotation computation for triangle and hexahedron  elements.

And the human implemented examples, comparison and benchmarks with the current implementation of FEM in SofaCUDA.

As for the bench (only for tet and hex):
In a nutshell,

• the legacy Tetrahedron version is very specialized/optimized so is quite faster than the new one (more elements there are faster it is)
• nevertheless, the Hexahedron version is opposite: the new one is faster than the legacy, more elements they are, faster it is.

Benches (only corotational...)
(i7 13700K + 4080Ti)
can be launched like that :

for version in new legacy; do for template in Vec3d CudaVec3f CudaVec3d; do NX=40 NY=10 NZ=10 NBSTEPS=1000 FEM_VERSION=$version FEM_TEMPLATE=$template python ../../../src/sandbox/applications/plugins/SofaCUDA/examples/ElementFEMForcefield/benchmarks/Hexahedron_corotational.py | grep "steps done in";   done; done

LinearSolver is CG, 250 steps, tol=1e-12

40x10x10 grid (1000 steps, 4000 nodes, 3159 hexa )

HexahedronFEM: version=new template=Vec3d grid=(40, 10, 10) | 1000 steps done in 16.1s (62.019 fps).
HexahedronFEM: version=new template=CudaVec3f grid=(40, 10, 10) | 1000 steps done in 6.0s (166.63 fps).
HexahedronFEM: version=new template=CudaVec3d grid=(40, 10, 10) | 1000 steps done in 7.17s (139.38 fps).
HexahedronFEM: version=legacy template=Vec3d grid=(40, 10, 10) | 1000 steps done in 57.4s (17.413 fps).
HexahedronFEM: version=legacy template=CudaVec3f grid=(40, 10, 10) | 1000 steps done in 7.26s (137.71 fps).
HexahedronFEM: version=legacy template=CudaVec3d grid=(40, 10, 10) | 1000 steps done in 65.6s (15.253 fps).
---
TetrahedronFEM: version=new template=Vec3d grid=(40, 10, 10) | 1000 steps done in 31.6s (31.661 fps).
TetrahedronFEM: version=new template=CudaVec3f grid=(40, 10, 10) | 1000 steps done in 6.42s (155.66 fps).
TetrahedronFEM: version=new template=CudaVec3d grid=(40, 10, 10) | 1000 steps done in 8.31s (120.36 fps).
TetrahedronFEM: version=legacy template=Vec3d grid=(40, 10, 10) | 1000 steps done in 88.5s (11.298 fps).
TetrahedronFEM: version=legacy template=CudaVec3f grid=(40, 10, 10) | 1000 steps done in 5.28s (189.25 fps).
TetrahedronFEM: version=legacy template=CudaVec3d grid=(40, 10, 10) | 1000 steps done in 6.42s (155.79 fps).

76x16x16 grid (1000 steps, 19456 nodes, 16875 hexa ) (no cpu)

HexahedronFEM: version=new template=CudaVec3f grid=(76, 16, 16) | 1000 steps done in 11.9s (83.914 fps).
HexahedronFEM: version=new template=CudaVec3d grid=(76, 16, 16) | 1000 steps done in 21.1s (47.282 fps).
HexahedronFEM: version=legacy template=CudaVec3f grid=(76, 16, 16) | 1000 steps done in 21.5s (46.525 fps).
HexahedronFEM: version=legacy template=CudaVec3d grid=(76, 16, 16) | 1000 steps done in 9.35e+02s (1.07 fps).
---
TetrahedronFEM: version=new template=CudaVec3f grid=(76, 16, 16) | 1000 steps done in 17.9s (55.988 fps).
TetrahedronFEM: version=new template=CudaVec3d grid=(76, 16, 16) | 1000 steps done in 58.8s (17.007 fps).
TetrahedronFEM: version=legacy template=CudaVec3f grid=(76, 16, 16) | 1000 steps done in 10.4s (95.943 fps).
TetrahedronFEM: version=legacy template=CudaVec3d grid=(76, 16, 16) | 1000 steps done in 17.9s (55.955 fps).

For the fun, the hexa new version with the a 200x30x30 (180k points, 167k hexa) and a downgraded CG (50 steps, tol of 1e-06) :
1000 iterations done in 65.5718 s ( 15.2504 FPS)

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• it builds with SUCCESS for all platforms on the CI.
• it does not generate new warnings.
• it does not generate new unit test failures.
• it does not generate new scene test failures.
• it does not break API compatibility.
• it is more than 1 week old (or has fast-merge label).

[alxbilger]

A criticism is that the code supposes that the space is in 3D. There are also some dynamic checks on the number of nodes per element. But this data is constexpr.

[fredroy]

A criticism is that the code supposes that the space is in 3D. There are also some dynamic checks on the number of nodes per element. But this data is constexpr.

Taken into account by 🤖