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

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  • Fazal Ghaffar
  • Noor Badshah
  • Saeed Islam

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 l2.

Suggested Citation

  • Fazal Ghaffar & Noor Badshah & Saeed Islam, 2014. "Multigrid Method for Solution of 3D Helmholtz Equation Based on HOC Schemes," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:954658
    DOI: 10.1155/2014/954658
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