Time space domain decomposition for reactive transport

Abstract

In this paper, we apply a Schwarz waveform relaxation method to a two-species reactive transport system. By Fourier analysis we find optimal coupling conditions that result in pseudo-differential operators. We approximate these operators by differential operators and give an upper bound for the convergence rate. By this technique a best approximation problem arises that is solved numerically. We finally obtain an optimised transmission condition that we will analyse numerically.

This result is a first important theoretical issue for the application of domain decomposition methods to large coupled systems of reactive transport equations and has a great implication on the global performance of the numerical approach.