Preconditioning harmonic unsteady potential flow calculations
This paper considers finite element discretizations of the Helmholtz equation and its generalization arising from harmonic acoustic perturbations to a nonuniform steady potential flow. A novel elliptic, positive-definite preconditioner with a multigrid implementation is used to accelerate the iterat...
| Príomhchruthaitheoirí: | , |
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| Formáid: | Journal article |
| Teanga: | English |
| Foilsithe / Cruthaithe: |
2006
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| _version_ | 1826284061897785344 |
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| author | Laird, A Giles, M |
| author_facet | Laird, A Giles, M |
| author_sort | Laird, A |
| collection | OXFORD |
| description | This paper considers finite element discretizations of the Helmholtz equation and its generalization arising from harmonic acoustic perturbations to a nonuniform steady potential flow. A novel elliptic, positive-definite preconditioner with a multigrid implementation is used to accelerate the iterative convergence of Krylov subspace solvers. Both theory and numerical results show that for a model 1-D Helmholtz test problem, the preconditioner clusters the discrete system's eigenvalues and lowers its condition number to a level independent of grid resolution. For the 2-D Helmholtz equation, grid-independent convergence is achieved using a quasi-minimal residual Krylov solver, significantly outperforming the popular symmetric successive over-relaxation preconditioner. Impressive results are also presented on more complex domains, including an axisymmetric aircraft engine inlet with nonstagnant mean flow and modal boundary conditions. Copyright © 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. |
| first_indexed | 2024-03-07T01:08:12Z |
| format | Journal article |
| id | oxford-uuid:8c12e05f-7a1c-4abf-b9e3-1c81f52ae7c4 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:08:12Z |
| publishDate | 2006 |
| record_format | dspace |
| spelling | oxford-uuid:8c12e05f-7a1c-4abf-b9e3-1c81f52ae7c42022-03-26T22:42:17ZPreconditioning harmonic unsteady potential flow calculationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:8c12e05f-7a1c-4abf-b9e3-1c81f52ae7c4EnglishSymplectic Elements at Oxford2006Laird, AGiles, MThis paper considers finite element discretizations of the Helmholtz equation and its generalization arising from harmonic acoustic perturbations to a nonuniform steady potential flow. A novel elliptic, positive-definite preconditioner with a multigrid implementation is used to accelerate the iterative convergence of Krylov subspace solvers. Both theory and numerical results show that for a model 1-D Helmholtz test problem, the preconditioner clusters the discrete system's eigenvalues and lowers its condition number to a level independent of grid resolution. For the 2-D Helmholtz equation, grid-independent convergence is achieved using a quasi-minimal residual Krylov solver, significantly outperforming the popular symmetric successive over-relaxation preconditioner. Impressive results are also presented on more complex domains, including an axisymmetric aircraft engine inlet with nonstagnant mean flow and modal boundary conditions. Copyright © 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. |
| spellingShingle | Laird, A Giles, M Preconditioning harmonic unsteady potential flow calculations |
| title | Preconditioning harmonic unsteady potential flow calculations |
| title_full | Preconditioning harmonic unsteady potential flow calculations |
| title_fullStr | Preconditioning harmonic unsteady potential flow calculations |
| title_full_unstemmed | Preconditioning harmonic unsteady potential flow calculations |
| title_short | Preconditioning harmonic unsteady potential flow calculations |
| title_sort | preconditioning harmonic unsteady potential flow calculations |
| work_keys_str_mv | AT lairda preconditioningharmonicunsteadypotentialflowcalculations AT gilesm preconditioningharmonicunsteadypotentialflowcalculations |