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2014 Multigrid Method for Solution of 3D Helmholtz Equation Based on HOC Schemes
Fazal Ghaffar, Noor Badshah, Saeed Islam
Abstr. Appl. Anal. 2014(SI51): 1-14 (2014). DOI: 10.1155/2014/954658


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 .


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Fazal Ghaffar. Noor Badshah. Saeed Islam. "Multigrid Method for Solution of 3D Helmholtz Equation Based on HOC Schemes." Abstr. Appl. Anal. 2014 (SI51) 1 - 14, 2014.


Published: 2014
First available in Project Euclid: 27 February 2015

zbMATH: 07023394
MathSciNet: MR3256268
Digital Object Identifier: 10.1155/2014/954658

Rights: Copyright © 2014 Hindawi


Vol.2014 • No. SI51 • 2014
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