Simulation of reaction-diffusion processes in three dimensions using CUDA

TL;DR

This paper demonstrates how GPU-based parallel computing with CUDA significantly accelerates the numerical simulation of complex reaction-diffusion processes in three dimensions, making such computations more feasible.

Contribution

It introduces a CUDA-based parallel framework for reaction-diffusion simulations and compares two GPU methods, achieving substantial speedups over CPU implementations.

Findings

GPU implementation accelerates simulations by 5-40 times

Four different reaction-diffusion problems were successfully solved

Shared and Moving Tiles methods were tested and compared

Abstract

Numerical solution of reaction-diffusion equations in three dimensions is one of the most challenging applied mathematical problems. Since these simulations are very time consuming, any ideas and strategies aiming at the reduction of CPU time are important topics of research. A general and robust idea is the parallelization of source codes/programs. Recently, the technological development of graphics hardware created a possibility to use desktop video cards to solve numerically intensive problems. We present a powerful parallel computing framework to solve reaction-diffusion equations numerically using the Graphics Processing Units (GPUs) with CUDA. Four different reaction-diffusion problems, (i) diffusion of chemically inert compound, (ii) Turing pattern formation, (iii) phase separation in the wake of a moving diffusion front and (iv) air pollution dispersion were solved, and additionally both the Shared method and the Moving Tiles method were tested. Our results show that parallel implementation achieves typical acceleration values in the order of 5-40 times compared to CPU using a single-threaded implementation on a 2.8 GHz desktop computer.