SEBSM-Based Iterative Method for Solving Large Systems of Linear Equations and Its Applications in Engineering Computation

Abstract

In this paper, a new iterative method, for solving sparse nonsymmetrical systems of linear equations is proposed based on the Simultaneous Elimination and Back-Substitution Method (SEBSM), and the method is applied to solve systems resulted in engineering problems solved using Finite Element Method (FEM). First, SEBSM is introduced for solving general linear systems using the direct method. And, then an iterative method based on SEBSM is presented. In the method, the coefficient matrix [Formula: see text] is split into lower, diagonally banded and upper matrices. The iterative convergence can be controlled by selecting a suitable bandwidth of the diagonally banded matrix. And the size of the working array needing to be stored in iteration is as small as the bandwidth of the diagonally banded matrix. Finally, an accelerating strategy for this iterative method is proposed by introducing a relaxation factor, which can speed up the convergence effectively if an optimal relaxation factor is chosen. Two numerical examples are given to demonstrate the behavior of the proposed method.