Apllying stochastic process to domain decomposition method

Abstract

We consider the problem of solving the algebraic system of equations which arise from the discretization of symmetric elliptic boundary value problems via finite element methods.A new class of preconditioners for these discrete system is developed based on substructuring (also known as domain decomposition). The resulting preconditioned methods are well suited to emerging parallel computing architectures. The proposed methods are applicable to problems on general domains involving differential operators with rather general coefficients. We see a numerical result of this method.