Simulation of reaction–diffusion processes in three dimensions using CUDA

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 * Corresponding author. Tel.: +36-2090555; fax: +36-1372-2904. 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.

Evolving Reaction-Diffusion Systems on GPU

“…Besides reaction and diffusion, these systems take into account advection phenomena in which chemicals also move by fluid transport, such as pollutants in the air or water. An implementation of reaction-diffusion in three dimensions is reported in [20]. Accompanying source code is publicly available for both [20,24], however both are far more elaborate than what we needed for our own experiments.…”

“…An implementation of reaction-diffusion in three dimensions is reported in [20]. Accompanying source code is publicly available for both [20,24], however both are far more elaborate than what we needed for our own experiments. Moreover, none of these implementations covered the execution and fitness evaluation of multiple reactiondiffusion individuals in parallel on the same GPU card.…”

“…Whereas the numeric integration of RD PDEs is already computationally expensive, evolving a population of these PDEs is even more demanding. Luckily, both GP and RD numeric integration are well suited for parallelization on top of GPU (Graphics Processing Unit) hardware [2,16,20,24].…”

Visual Simulation of Soil-Microbial System Using GPGPU Technology

“…A class of application for which this is true, and one particularly relevant to soil ecosystem models, is the Reaction-Diffusion system. Reaction-Diffusion systems have been implemented on GPU for procedural texture generation, pollution dispersal and phase separation [15][16][17].…”

Dispersion modeling of air pollutants in the atmosphere: a review

“…Multicore workstations [105] and the recently developed technology of using graphics processors (GPUs) for general purpose computation (GPGPU, [106]) are examples of shared memory systems. GPU computing has been successfully applied in atmospheric dispersion modeling [107,111] as well as in closely related fields [112][113][114][115][116]. Depending on the type of computation, the GPU's speedup over a single CPU can be one or two orders of magnitude [117,118], and accordingly, a single high-end video card can compete with a smaller cluster of computers.…”