Studies of an interface relaxation domain decomposition technique using finite elements on a parallel computer

Abstract

AbstractStudies are presented for an interface relaxation domain decomposition technique using finite elements on an iPSC/2 D5 Hypercube Concurrent computer. The general type of problem to be solved is one governed by a partial differential equation. The application of the approach, however, will be extended to a free boundary value problem by appropriate modification of the numerical scheme. Using the domain decomposition technique, the computation domain is subdivided into several subdomains. In addition, on the interfaces between two adjacent subdomains are imposed a continuity condition on one side and an equilibrium condition on the other side. Successive overrelaxation iterative processes are then carried out in all subdomains with a relaxation process imposed on the interfaces. With this domain decomposition technique, the problem can be solved parallelly until convergence is reached both in the interiors and on the interfaces of all subdomains. Moreover, the formulation includes a simple domain decomposer that automatically divides a finite element mesh into a list of subdomains to guarantee load balancing. Furthermore, it is shown, through numerical experiments performed on an example problem of free surface seepage through a porous dam, how the values of the relaxation parameters, the choice of imposed boundary conditions, and the number of subdomains (i.e., the number of processors used) affect the solution convergence in this parallel computing environment. © 1993 John Wiley & Sons, Inc.