A New Domain Decomposition Parallel Algorithm for Convection–Diffusion Problem

Abstract

Basing on overlapping domain decomposition, we construct a new parallel algorithm combined the method of subspace correction with least-squares procedure for solving time-dependent convection–diffusion problem. This algorithm is fully parallel. We analyze the convergence of approximate solution, and study the dependence of the convergent rate on the spacial mesh size, time increment, iteration number and sub-domains overlapping degree. Both theoretical analysis and numerical results suggest that only one or two iterations are needed to reach to given accuracy at each time step.

Keywords:

• parallel algorithm
• finite element method
• convection-diffusion problem
• convergence analysis

AMS Subject Classification:

• 65M55
• 65M60