README.md

2024LJKL

Codex/ChatGPT (July 2026)

Summary

This paper develops a GPU backend for the adaptive finite element library Gascoigne 3d, targeting geometric multigrid solvers on locally refined meshes. Rather than redesigning the discretization around GPU-specific kernels, the implementation maps existing dense and sparse linear algebra operations to cuBLAS and cuSPARSE and wraps the library's data interfaces to limit host-device transfers. Custom CUDA kernels are used only where they remove bottlenecks, such as right-hand-side assembly. The approach is tested on transport-diffusion, linear elasticity, and instationary Navier-Stokes problems, showing substantial speedups, in some cases up to about $20\times$ relative to multicore CPU runs. The experiments also identify limits: sparse matrix operations already reach high memory bandwidth, thousands of small kernel calls constrain further gains, and CPU-side matrix assembly restricts nonlinear applications. The paper argues that a conservative linear-algebra-based GPU port can deliver useful acceleration while keeping the CPU and GPU code paths maintainable.

Contributions

1. Added GPU acceleration to an adaptive finite element multigrid code with limited code-path divergence.
2. Mapped finite element solver operations mainly to cuBLAS and cuSPARSE primitives.
3. Encapsulated data movement through custom Gascoigne 3d interface implementations.
4. Benchmarked transport-diffusion, elasticity, and Navier-Stokes examples on adaptive meshes.
5. Identified remaining bottlenecks from CPU assembly, sparse-kernel memory bandwidth, and kernel-call granularity.