Multigrid Method for Solution of 3D Helmholtz Equation Based on HOC Schemes

Fazal Ghaffar, Noor Badshah and Saeed Islam

Abstract and Applied Analysis, 2014, vol. 2014, 1-14

Abstract:

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 .

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:954658

DOI: 10.1155/2014/954658

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