An efficient storage technique for parallel Schur complement method and applications on different platforms

Abstract

Parallel solution of large-scale problems attracted attention of many researchers more than a decade for which efficient solution techniques are being sought continuously. Due to advances in computer hardware, either new techniques are being proposed or many of the existing techniques are modified to exploit the advantages of new computer architectures. One of the existing methods used to solve large-scale problems is a substructuring technique known as the Schur complement method in the literature. In this chapter, a parallel Schur complement method is implemented for solution of elliptic equations. After decomposition of the total domain into subdomains, interface equations are expressed in a coupled form with the subdomain equations. The solution of subdomains is performed after solving the interface equations. This chapter presents an efficient formation of interface and subdomain equations in parallel environments using direct solvers, which take into account sparse and banded structures of the subdomain coefficient matrices. With such an approach, one is able to solve larger system of equations. Test cases are presented on different platforms to illustrate the performance of the algorithm.