First working GPU assembly implementation (proof-of-concept stage)
demonstrating complete FEM solve staying on GPU for 2D elasticity.
Implementation:
- Element-parallel GPU kernel for Quad4 elements
- 2×2 Gauss quadrature on GPU
- Plain vector approach (before Tensors.jl integration)
- Matrix-free Jacobian-vector product
- Complete Newton-Krylov loop on GPU
- BC enforcement via masking
Test case: 10×10 Quad4 mesh (100 elements, 242 DOFs)
- Material: Steel (E=200 GPa, ν=0.3)
- BC: Fixed left edge, displacement on right edge
Architecture validation:
- GPU assembly matches CPU (error < 1e-15)
- Entire solve stays on GPU (no ping-pong)
- Only transfers: mesh (once) + u0/u_final (boundary)
Note: This is the initial version using plain vectors and manual
indexing. See gpu_assembly_poc_tensors.jl for corrected version
using proper Tensors.jl material API (606 lines).
Jukka Aho