A GPU accelerated mixed-precision Finite Difference informed Random Walker (FDiRW) solver for strongly inhomogeneous diffusion problems

TL;DR

This paper introduces a GPU-accelerated, mixed-precision FDiRW solver that significantly speeds up simulations of inhomogeneous diffusion problems, enabling larger and more complex models to be computed efficiently.

Contribution

The paper presents a novel GPU-accelerated, mixed-precision implementation of the FDiRW solver, achieving substantial speedups and scalability for strongly inhomogeneous diffusion simulations.

Findings

117X speedup over CPU baseline

1.75X additional speedup with lower precision GPU computation

Effective strong scaling with increased GPU nodes

Abstract

In nature, many complex multi-physics coupling problems exhibit significant diffusivity inhomogeneity, where one process occurs several orders of magnitude faster than others in temporal. Simulating rapid diffusion alongside slower processes demands intensive computational resources due to the necessity for small time steps. To address these computational challenges, we have developed an efficient numerical solver named Finite Difference informed Random Walker (FDiRW). In this study, we propose a GPU-accelerated, mixed-precision configuration for the FDiRW solver to maximize efficiency through GPU multi-threaded parallel computation and lower precision computation. Numerical evaluation results reveal that the proposed GPU-accelerated mixed-precision FDiRW solver can achieve a 117X speedup over the CPU baseline, while an additional 1.75X speedup by employing lower precision GPU computation. Notably, for large model sizes, the GPU-accelerated mixed-precision FDiRW solver demonstrates strong scaling with the number of nodes used in simulation. When simulating radionuclide absorption processes by porous wasteform particles with a medium-sized model of 192x192x192, this approach reduces the total computational time to 10 minutes, enabling the simulation of larger systems with strongly inhomogeneous diffusivity.