Distributed algebraic tearing and interconnecting techniques

Abstract

A class of novel parallel preconditioning schemes in conjunction with a Krylov subspace iterative method for solving general sparse linear systems is presented. The proposed preconditioning schemes are domain decomposition methods that enforce the continuity of the solution on the subdomain interfaces using Lagrange multipliers, without requiring geometric information, namely algebraic tearing and interconnecting methods. Hence, they are applicable to a wide variety of problems as they are based only on the adjacency graph corresponding to the coefficient matrix. A modification of the proposed schemes, which improves performance while reducing the required operations is also presented. The algebraic tearing and interconnecting methods are designed for distributed systems with multicore nodes. Numerical results concerning the convergence behavior and the parallel performance of the proposed schemes are given along with discussions.