Multigrid method for solution of 3D Helmholtz equation based on HOC schemes. (English) Zbl 1474.65420

Ghaffar, Fazal; Badshah, Noor; Islam, Saeed

Abstr. Appl. Anal. 2014, Article ID 954658, 14 p. (2014).

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 \(l_2\).

MSC:

65N06	Finite difference methods for boundary value problems involving PDEs
65F10	Iterative numerical methods for linear systems
65N22	Numerical solution of discretized equations for boundary value problems involving PDEs
65N55	Multigrid methods; domain decomposition for boundary value problems involving PDEs
35J05	Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation

Software:

Wesseling

References:

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