Multigrid method for solution of 3D Helmholtz equation based on HOC schemes
type: Item
instance of: scholarly article
title: Multigrid method for solution of 3D Helmholtz equation based on HOC schemes
zbMATH Open document ID: 1474.65420
DOI: 10.1155/2014/954658
author: Fazal Ghaffar
author: Noor Badshah
author: S. Islam
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: A higher order compact difference (HOC) scheme with uniform mesh sizes in different coordinate directions is employed to discretize a two- and three-dimensional Helmholtz equation. In case of two dimension, the stencil is of 9 points while in three-dimensional case, the scheme has 27 points and has fourth- to fifth-order accuracy. Multigrid method using Gauss-Seidel relaxation is designed to solve the resulting sparse linear systems. Numerical experiments were conducted to test the accuracy of the sixth-order compact difference scheme with Multigrid method and to compare it with the standard second-order finite-difference scheme and fourth-order compact difference scheme. Performance of the scheme is tested through numerical examples. Accuracy and efficiency of the new scheme are established by using the errors norms \(l_2\).
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65N22
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 7023394
Wikidata QID: Q59043104
describes a project that uses: Wesseling
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/954658
OpenAlex ID: W2108201315
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description: scientific article; zbMATH DE number 7023394