The construction of preconditioners for elliptic problems by substructuring. IV

Abstract

We consider the problem of solving the algebraic system of equations which result from the discretization of elliptic boundary value problems defined on three-dimensional Euclidean space. We develop preconditioners for such systems based on substructuring (also known as domain decomposition). The resulting algorithms are well suited to emerging parallel computing architectures. We describe two techniques for developing these preconditioners. A theory for the analysis of the condition number for the resulting preconditioned system is given and the results of supporting numerical experiments are presented.