Accelerating the Finite-Element Method for Reaction-Diffusion Simulations on GPUs with CUDA

Abstract

DNA nanotechnology offers a fine control over biochemistry by programming chemical reactions in DNA templates. Coupled to microfluidics, it has enabled DNA-based reaction-diffusion microsystems with advanced spatio-temporal dynamics such as traveling waves. The Finite Element Method (FEM) is a standard tool to simulate the physics of such systems where boundary conditions play a crucial role. However, a fine discretization in time and space is required for complex geometries (like sharp corners) and highly nonlinear chemistry. Graphical Processing Units (GPUs) are increasingly used to speed up scientific computing, but their application to accelerate simulations of reaction-diffusion in DNA nanotechnology has been little investigated. Here we study reaction-diffusion equations (a DNA-based predator-prey system) in a tortuous geometry (a maze), which was shown experimentally to generate subtle geometric effects. We solve the partial differential equations on a GPU, demonstrating a speedup of ∼100 over the same resolution on a 20 cores CPU.

Editorial on the Special Issue on Recent Advances of Molecular Machines and Molecular Robots

“…In this Special Issue, six research papers and two review articles related to molecular machine engineering and molecular robotics from a wide range of research fields have been presented. Three theoretical research papers, on reaction-diffusion simulation accelerated the finite-element method by Sellami et al [4], on a structural design of conjugated proton cranes based on the density functional theory (DFT) by Georgiev et al [5], and on the modeling of mesh structure for a microtubule filament by Ueno et al [6], will contribute the design for the molecular machines/robots. The other three research papers will be an insight into the construction or motion of molecular machines/robots.…”