Rocky Mountain Journal of Mathematics

A geometric full multigrid method and fourth-order compact scheme for the 3D Helmholtz equation on nonuniform grid discretization

Zhenwei Yang, Xiaobin Li, Lei Feng, and Xinxin Hou

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Abstract

A full multigrid method and fourth-order compact difference scheme is designed to solve the 3D Helmholtz equation on unequal mesh size. Three dimensional restriction and prolongation operators of the multigrid method on unequal grids could be constructed based on volume law. Two numerical experiments are implemented, and the results show the computational efficiency and accuracy of the full multigrid method. The study also illustrates that the full multigrid method with fourth-order compact difference scheme has great advantages in computation, which has been time consuming, and in iterative convergence efficiency.

Article information

Source
Rocky Mountain J. Math., Volume 49, Number 3 (2019), 1029-1047.

Dates
First available in Project Euclid: 23 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1563847246

Digital Object Identifier
doi:10.1216/RMJ-2019-49-3-1029

Mathematical Reviews number (MathSciNet)
MR3983313

Zentralblatt MATH identifier
07088349

Subjects
Primary: 65F10: Iterative methods for linear systems [See also 65N22]
Secondary: 65N06: Finite difference methods 65N55: Multigrid methods; domain decomposition

Keywords
Full multigrid method Helmholtz equation restriction operator nonuniform grid

Citation

Yang, Zhenwei; Li, Xiaobin; Feng, Lei; Hou, Xinxin. A geometric full multigrid method and fourth-order compact scheme for the 3D Helmholtz equation on nonuniform grid discretization. Rocky Mountain J. Math. 49 (2019), no. 3, 1029--1047. doi:10.1216/RMJ-2019-49-3-1029. https://projecteuclid.org/euclid.rmjm/1563847246


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