A novel multigrid based preconditioner for heterogeneous Helmholtz problems

被引：215
作者：
Erlangga, Y [1 ]
Oosterlee, C [1 ]
Vuik, C [1 ]
机构：
[1] Delft Univ Technol, Fac Elect Engn Math & Comp Sci, Delft, Netherlands
来源：
SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2006年 / 27卷 / 04期
关键词：
Helmholtz equation; nonconstant high wavenumber; complex multigrid preconditioner; Fourier analysis;
D O I：
10.1137/040615195
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An iterative solution method, in the form of a preconditioner for a Krylov subspace method, is presented for the Helmholtz equation. The preconditioner is based on a Helmholtz-type differential operator with a complex term. A multigrid iteration is used for approximately inverting the preconditioner. The choice of multigrid components for the corresponding preconditioning matrix with a complex diagonal is validated with Fourier analysis. Multigrid analysis results are verified by numerical experiments. High wave number Helmholtz problems in heterogeneous media are solved indicating the performance of the preconditioner.
引用
收藏
页码：1471 / 1492
页数：22
相关论文
共 31 条
  • [1] THE MULTI-GRID METHOD FOR THE DIFFUSION EQUATION WITH STRONGLY DISCONTINUOUS COEFFICIENTS
    ALCOUFFE, RE
    BRANDT, A
    DENDY, JE
    PAINTER, JW
    [J]. SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1981, 2 (04): : 430 - 454
  • [2] [Anonymous], 2003, ITERATIVE METHODS SP, DOI DOI 10.1137/1.9780898718003
  • [3] 2ND-ORDER ABSORBING BOUNDARY-CONDITIONS FOR THE WAVE-EQUATION - A SOLUTION FOR THE CORNER PROBLEM
    BAMBERGER, A
    JOLY, P
    ROBERTS, JE
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1990, 27 (02) : 323 - 352
  • [4] ON ACCURACY CONDITIONS FOR THE NUMERICAL COMPUTATION OF WAVES
    BAYLISS, A
    GOLDSTEIN, CI
    TURKEL, E
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 1985, 59 (03) : 396 - 404
  • [5] AN ITERATIVE METHOD FOR THE HELMHOLTZ-EQUATION
    BAYLISS, A
    GOLDSTEIN, CI
    TURKEL, E
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 1983, 49 (03) : 443 - 457
  • [6] Bourgeois A., 1991, MARMOUSI EXPERIENCE, P5, DOI DOI 10.3997/2214-4609.201411190
  • [7] BRACKENRIDGE K, 1993, P 6 ANN COPP MOUNT C, P31
  • [8] BRANDT A, 1977, MATH COMPUT, V31, P333, DOI 10.1090/S0025-5718-1977-0431719-X
  • [9] BRANDT A, 1984, GDM STUDIES, V85
  • [10] Brandt A., 1997, ELECTRON T NUMER ANA, V6, P162
1234