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

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.