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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832566621917413376 |
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| author | Fazal Ghaffar Noor Badshah Saeed Islam |
| author_facet | Fazal Ghaffar Noor Badshah Saeed Islam |
| author_sort | Fazal Ghaffar |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-77ae71371f6e4828b8fd70e27c0c3387 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-77ae71371f6e4828b8fd70e27c0c33872025-02-03T01:03:37ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/954658954658Multigrid Method for Solution of 3D Helmholtz Equation Based on HOC SchemesFazal Ghaffar0Noor Badshah1Saeed Islam2Department of Mathematics, Abdul Wali Khan University Mardan, PakistanDepartment of Basic Sciences, UET, Peshawar, PakistanDepartment of Mathematics, Abdul Wali Khan University Mardan, PakistanA 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.http://dx.doi.org/10.1155/2014/954658 |
| spellingShingle | Fazal Ghaffar Noor Badshah Saeed Islam Multigrid Method for Solution of 3D Helmholtz Equation Based on HOC Schemes Abstract and Applied Analysis |
| title | Multigrid Method for Solution of 3D Helmholtz Equation Based on HOC Schemes |
| title_full | Multigrid Method for Solution of 3D Helmholtz Equation Based on HOC Schemes |
| title_fullStr | Multigrid Method for Solution of 3D Helmholtz Equation Based on HOC Schemes |
| title_full_unstemmed | Multigrid Method for Solution of 3D Helmholtz Equation Based on HOC Schemes |
| title_short | Multigrid Method for Solution of 3D Helmholtz Equation Based on HOC Schemes |
| title_sort | multigrid method for solution of 3d helmholtz equation based on hoc schemes |
| url | http://dx.doi.org/10.1155/2014/954658 |
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