Toward a Multi-GPU Implementation of a GMRES Solver in CHAMPS

The Computational Fluid Dynamics (CFD) community has successfully leveraged GPUs for their solvers. In the industry, low-order solvers are often used because only engineering levels of accuracy are needed. Unlike high-order methods, these solvers don’t have high ratios of floating point operations per memory fetches but can still make good use of GPUs because of the high number of elements computed and higher memory bandwidth of those types of hardware. These solvers often use solvers that were designed to be optimal for CPUs with sequential parts like the Symmetric Gauss Seidel (SGS) solver. In an attempt to adapt to the hardware architecture and to better utilize the computational power of the GPU, a Jacobian-free Newton-Krylov (JFNK) type of solver is envisioned. The JFNK solver makes use of the fact that only the effect of the Jacobian on a vector is needed, hence removing the need to store and inverse the Jacobian matrix. Instead, a finite-difference approximation is computed. This paper discusses the early implementation of such a solver by showing the performance on the GPU of a GMRES solver (with Jacobian) developed in CHAMPS, a 3D unstructured RANS solver written in Chapel. The performance is evaluated by presenting speedups and a strong scaling analysis of the method. CCS CONCEPTS •Computingmethodologies→Massively parallel algorithms; Distributed algorithms; Parallel programming languages; •Applied computing → Computer-aided design.