Two Block Splitting Iteration Methods for Solving Complex Symmetric Linear Systems from Complex Helmholtz Equation

Yanan Zhu, Naimin Zhang () and Zhen Chao
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Yanan Zhu: College of Mathematics and Physics, Wenzhou University, Wenzhou 325035, China
Naimin Zhang: College of Mathematics and Physics, Wenzhou University, Wenzhou 325035, China
Zhen Chao: Department of Mathematics, Western Washington University, Bellingham, WA 98225, USA

Mathematics, 2024, vol. 12, issue 12, 1-22

Abstract: In this paper, we study the improved block splitting (IBS) iteration method and its accelerated variant, the accelerated improved block splitting (AIBS) iteration method, for solving linear systems of equations stemming from the discretization of the complex Helmholtz equation. We conduct a comprehensive convergence analysis and derive optimal iteration parameters aimed at minimizing the spectral radius of the iteration matrix. Through numerical experiments, we validate the efficiency of both iteration methods.

Keywords: complex Helmholtz equation; complex linear system; iteration method; optimal parameter; convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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