A fast solver for systems of reaction-diffusion equations

TL;DR

This paper introduces a rapid numerical algorithm for solving large, stiff systems of reaction-diffusion equations, which are crucial in modeling atmospheric chemistry and air pollution scenarios.

Contribution

The paper presents a novel fast solver specifically designed for large, stiff reaction-diffusion systems, improving computational efficiency in relevant applications.

Findings

Achieves significant speedup over traditional methods

Handles large vector-valued systems with high efficiency

Applicable to real-world atmospheric chemistry models

Abstract

In this paper we present a fast algorithm for the numerical solution of systems of reaction-diffusion equations, $\partial_t u + a \cdot \nabla u = \Delta u + F (x, t, u)$, $x \in \Omega \subset \mathbf{R}^3$, $t > 0$. Here, $u$ is a vector-valued function, $u \equiv u(x, t) \in \mathbf{R}^m$, $m$ is large, and the corresponding system of ODEs, $\partial_t u = F(x, t, u)$, is stiff. Typical examples arise in air pollution studies, where $a$ is the given wind field and the nonlinear function $F$ models the atmospheric chemistry.