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

Abstract EN

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 .