Evaluation of Different Approaches to Solution of the Direct Solution of Large, Sparse Systems of Linear Equations

Abstract

The aim of this paper is to the evaluate efficiency of differentapproaches to solution of large, sparse, non-symmetric systems of linearequations on high performance machines, that can be found in any finiteelement software. The different approaches based on direct or iterativealgorithms for solution of linear equations are compared. In particular,directs solver using Skyline sparse storage, direct solver from SuperLUlibrary, iterative solver from Iterative Method Library(IML)are compared. SuperLU is a general purpose library for the directsolution of large, sparse, nonsymmetric systems of linear equations.Additionally, the performance and scalability of parallel SuperLU solveris studied, based on OpenMP. The paper shows thatparallelization can efficiently exploit the power of modern availablehardware, significantly reducing the needed computation time.The different strategies were implemented in OOFEM which is afree finite element code with object oriented architecture for solvingmechanical, transport and fluid mechanics problems that operates onvarious platforms.