Preconditioned iterative solution of the 2D Helmholtz equation
Using a finite element method to solve the Helmholtz equation leads to a sparse system of equations which in three dimensions is too large to solve directly. It is also non-Hermitian and highly indefinite and consequently difficult to solve iteratively. The approach taken in this paper is to precond...
| Main Authors: | , |
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| Format: | Report |
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Unspecified
2002
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| _version_ | 1797066995111297024 |
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| author | Laird, A Giles, M |
| author_facet | Laird, A Giles, M |
| author_sort | Laird, A |
| collection | OXFORD |
| description | Using a finite element method to solve the Helmholtz equation leads to a sparse system of equations which in three dimensions is too large to solve directly. It is also non-Hermitian and highly indefinite and consequently difficult to solve iteratively. The approach taken in this paper is to precondition this linear system with a new preconditioner and then solve it iteratively using a Krylov subspace method. Numerical analysis shows the preconditioner to be effective on a simple 1D test problem, and results are presented showing considerable convergence acceleration for a number of different Krylov methods for more complex problems in 2D, as well as for the more general problem of harmonic disturbances to a non-stagnant steady flow. |
| first_indexed | 2024-03-06T21:49:56Z |
| format | Report |
| id | oxford-uuid:4ae3ffd2-1b8c-44aa-8537-9d06080f6c08 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:49:56Z |
| publishDate | 2002 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:4ae3ffd2-1b8c-44aa-8537-9d06080f6c082022-03-26T15:40:19ZPreconditioned iterative solution of the 2D Helmholtz equationReporthttp://purl.org/coar/resource_type/c_93fcuuid:4ae3ffd2-1b8c-44aa-8537-9d06080f6c08Mathematical Institute - ePrintsUnspecified2002Laird, AGiles, MUsing a finite element method to solve the Helmholtz equation leads to a sparse system of equations which in three dimensions is too large to solve directly. It is also non-Hermitian and highly indefinite and consequently difficult to solve iteratively. The approach taken in this paper is to precondition this linear system with a new preconditioner and then solve it iteratively using a Krylov subspace method. Numerical analysis shows the preconditioner to be effective on a simple 1D test problem, and results are presented showing considerable convergence acceleration for a number of different Krylov methods for more complex problems in 2D, as well as for the more general problem of harmonic disturbances to a non-stagnant steady flow. |
| spellingShingle | Laird, A Giles, M Preconditioned iterative solution of the 2D Helmholtz equation |
| title | Preconditioned iterative solution of the 2D Helmholtz equation |
| title_full | Preconditioned iterative solution of the 2D Helmholtz equation |
| title_fullStr | Preconditioned iterative solution of the 2D Helmholtz equation |
| title_full_unstemmed | Preconditioned iterative solution of the 2D Helmholtz equation |
| title_short | Preconditioned iterative solution of the 2D Helmholtz equation |
| title_sort | preconditioned iterative solution of the 2d helmholtz equation |
| work_keys_str_mv | AT lairda preconditionediterativesolutionofthe2dhelmholtzequation AT gilesm preconditionediterativesolutionofthe2dhelmholtzequation |