Discrete-Time Accelerated Block Successive Overrelaxation Methods for Time-Dependent Stokes Equations

TL;DR

This paper introduces the DABSOR method, a new discrete-time waveform relaxation technique designed to efficiently solve linear differential-algebraic equations from discretized time-dependent Stokes equations, with proven convergence and optimality.

Contribution

The paper proposes the DABSOR method for linear DAEs from Stokes equations, providing a comprehensive theoretical analysis of its convergence and optimality, and validating its efficiency through numerical experiments.

Findings

DABSOR method converges for the class of linear DAEs from Stokes equations.

The method achieves optimal convergence rates under certain conditions.

Numerical experiments confirm the theoretical efficiency of DABSOR.

Abstract

To further study the application of waveform relaxation methods in fluid dynamics in actual computation, this paper provides a general theoretical analysis of discrete-time waveform relaxation methods for solving linear DAEs. A class of discrete-time waveform relaxation methods, named discrete-time accelerated block successive overrelaxation (DABSOR) methods, is proposed for solving linear DAEs derived from discretizing time-dependent Stokes equations in space by using "Method of Lines". The analysis of convergence property and optimality of the DABSOR method are presented in detail. The theoretical results and the efficiency of the DABSOR method are verified by numerical experiments.