An iterative solver for the 3D Helmholtz equation

被引：14

作者：

Belonosov, Mikhail ^{[1
]}

Dmitriev, Maxim ^{[2
]}

Kostin, Victor ^{[3
]}

Neklyudov, Dmitry ^{[3
]}

Tcheverda, Vladimir ^{[3
,4
]}

机构：

[1] Aramco Overseas Co BV, EXPEC ARC GRC Delft, Informaticalaan 6, NL-2628 ZD Delft, Netherlands

[2] Saudi Aramco, EXPEC Adv Res Ctr, Bldg 137, Dhahran 31311, Saudi Arabia

[3] SB RAS, Trofimuk Inst Petr Geol & Geophys, 3 Koptyug Ave, Novosibirsk 630090, Russia

[4] Kazakh British Tech Univ, 59 Tole Bi St, Alma Ata 480091, Kazakhstan

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2017年 / 345卷

关键词：

Acoustics; Modeling; Helmholtz equation; Iterative methods; Preconditioning; PERFECTLY MATCHED LAYER; DOMAIN;

D O I：

10.1016/j.jcp.2017.05.026

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We develop a frequency-domain iterative solver for numerical simulation of acoustic waves in 3D heterogeneous media. It is based on the application of a unique preconditioner to the Helmholtz equation that ensures convergence for Krylov subspace iteration methods. Effective inversion of the preconditioner involves the Fast Fourier Transform (FFT) and numerical solution of a series of boundary value problems for ordinary differential equations. Matrix-by-vector multiplication for iterative inversion of the preconditioned matrix involves inversion of the preconditioner and pointwise multiplication of grid functions. Our solver has been verified by benchmarking against exact solutions and a time-domain solver. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：330 / 344

页数：15

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