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Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 4

A new double-step method for solving complex Helmholtz equation

Tahereh Salimi Siahkolaei
Davod Khojasteh Salkuyeh
Pages
1245–1260
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The proposed method is compared theoretically and numerically with some existing methods.******************************************************************************

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We present a new double-step iteration method for solving the systems of linear equations that arise from finite difference discretizations of the complex Helmholtz equations.
📊
Key Findings & Data:Convergence analysis of the method is discussed.
💡
Conclusion & Impact:The proposed method is compared theoretically and numerically with some existing methods.******************************************************************************
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Complex Helmholtz equation · iterative method · complex linear systems

Abstract

We present a new double-step iteration method for solving the systems of linear equations that arise from finite difference discretizations of the complex Helmholtz equations. Convergence analysis of the method is discussed. An upper bound on the spectral radius of the iteration matrix of the method is presented and the parameter which minimizes this upper bound is computed. The proposed method is compared theoretically and numerically with some existing methods.******************************************************************************

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Cite This Article

Siahkolaei, T. S., Salkuyeh, D. K. (2022). A new double-step method for solving complex Helmholtz equation. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 4, 1245–1260. https://ajindex.com/articles/529595

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