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A multigrid method with reduced phase error for 2D damped Helmholtz equations
Author(s) -
Ahmed Mostak,
Zhang Chengjian
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7155
Subject(s) - multigrid method , mathematics , helmholtz equation , operator (biology) , compact finite difference , grid , helmholtz free energy , mathematical analysis , finite difference , fourier transform , finite difference method , partial differential equation , geometry , physics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene , boundary value problem
This paper deals with a new multigrid method with reduced phase error for solving 2D damped Helmholtz equations. The method is obtained by taking the high‐effective, reduced phase error 5‐point finite difference (FD) scheme as a coarse grid operator and the regular 5‐point FD scheme as a fine grid operator. It is found that the proposed method gives a faster convergent rate than the regular multigrid method. A local mode Fourier analysis confirms the validity of our proposed method. Finally, some numerical results demonstrate the efficiency of the method.