Multigrid Method for Solution of 3D Helmholtz Equation Based on HOC Schemes
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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/954658 |
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| 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 l2. |
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| ISSN: | 1085-3375 1687-0409 |