A parallel space-time domain decomposition method for unsteady source inversion problems

TL;DR

This paper introduces a parallel space-time domain decomposition method for efficiently solving unsteady source inversion problems governed by convection-diffusion equations, enabling scalable large-scale computations.

Contribution

It proposes a fully implicit space-time Schwarz preconditioner that improves parallel efficiency and scalability for large-scale unsteady source inversion problems.

Findings

The method effectively handles noisy data.

The parallel Schwarz preconditioner is scalable on supercomputers with over 1000 processors.

Numerical experiments confirm robustness and efficiency.

Abstract

In this paper, we propose a parallel space-time domain decomposition method for solving an unsteady source identification problem governed by the linear convection-diffusion equation. Traditional approaches require to solve repeatedly a forward parabolic system, an adjoint system and a system with respect to the unknowns. The three systems have to be solved one after another. These sequential steps are not desirable for large scale parallel computing. A space-time restrictive additive Schwarz method is proposed for a fully implicit space-time coupled discretization scheme to recover the time-dependent pollutant source intensity functions. We show with numerical experiments that the scheme works well with noise in the observation data. More importantly it is demonstrated that the parallel space-time Schwarz preconditioner is scalable on a supercomputer with over $10^3$ processors, thus promising for large scale applications.