Block-Based Approach to Solving Linear Systems

Abstract

Abstract. This paper addresses the efficiency issues in solving large sparse linear systems parallely on scalar and vector architectures. Linear systems arise in numerous applications that need to solve PDEs on complex domains. The major time consuming part of large scale implicit Finite Element (FE) or Finite Volume (FV) simulation is solving the assembled global system of equations. First, the performance of widely used public domain solvers which target performance on scalar machines is analyzed on a typical vector machine. Then, a newly developed parallel sparse iterative solver (Block-based Linear Iterative Solver -BLIS) targeting performance on both scalar and vector systems is introduced and the time needed for solving linear systems is compared on different architectures. Finally, the reasons behind the scaling behaviour of parallel iterative solvers is analysed.