A dispersion minimizing compact finite difference scheme for the 2D Helmholtz equation

被引：30

作者：

Wu, Tingting ^{[1
]}

机构：

[1] Shandong Normal Univ, Sch Math Sci, Jinan 250014, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2017年 / 311卷

关键词：

Helmholtz equation; Compact finite difference scheme; Numerical dispersion; SCALAR WAVE EXTRAPOLATOR; FREQUENCY-SPACE; OPTIMAL; 9-POINT; POLLUTION; NUMBERS; FEM;

D O I：

10.1016/j.cam.2016.08.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a dispersion minimizing compact finite difference scheme for solving the 2D Helmholtz equation, which is a fourth-order scheme. The error between the numerical wavenumber and the exact wavenumber is analyzed, and a refined choice strategy based on minimizing the numerical dispersion is proposed for choosing weight parameters. Numerical results are presented to demonstrate the efficiency and accuracy of the compact finite difference scheme with refined parameters. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：497 / 512

页数：16

共 15 条

[1] A Generalized Finite Element Method for solving the Helmholtz equation in two dimensions with minimal pollution [J].

Babuska, I ;

Ihlenburg, F ;

Paik, ET ;

Sauter, SA .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1995, 128 (3-4) :325-359

[2]

Babuska IM, 2000, SIAM REV, V42, P451

[3] Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media using Compact High Order Schemes [J].

Britt, Steven ;

Tsynkov, Semyon ;

Turkel, Eli .

COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2011, 9 (03) :520-541

[4]

Chen ZY, 2013, INT J NUMER ANAL MOD, V10, P389

[5] A dispersion minimizing finite difference scheme and preconditioned solver for the 3D Helmholtz equation [J].

Chen, Zhongying ;

Cheng, Dongsheng ;

Wu, Tingting .

JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 231 (24) :8152-8175

[6] An optimal 25-point finite difference scheme for the Helmholtz equation with PML [J].

Chen, Zhongying ;

Wu, Tingting ;

Yang, Hongqi .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 236 (06) :1240-1258

[7]

Fu YP, 2008, J COMPUT MATH, V26, P98

[8] ACCURATE FINITE-DIFFERENCE METHODS FOR TIME-HARMONIC WAVE-PROPAGATION [J].

HARARI, I ;

TURKEL, E .

JOURNAL OF COMPUTATIONAL PHYSICS, 1995, 119 (02) :252-270

[9] FINITE-ELEMENT SOLUTION OF THE HELMHOLTZ-EQUATION WITH HIGH WAVE-NUMBER .1. THE H-VERSION OF THE FEM [J].

IHLENBURG, F ;

BABUSKA, I .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1995, 30 (09) :9-37

[10] An optimal 9-point, finite-difference, frequency-space, 2-D scalar wave extrapolator [J].

Jo, CH ;

Shin, CS ;

Suh, JH .

GEOPHYSICS, 1996, 61 (02) :529-537

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