Optimal operator preconditioning for Galerkin boundary element methods on 3-dimensional screens
We consider first-kind weakly singular and hypersingular boundary integral operators for the Laplacian on screens in R3 and their Galerkin discretization by means of low-order piecewise polynomial boundary elements. For the resulting linear systems of equations we propose novel Calder´on-type precon...
| Egile Nagusiak: | , , |
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| Formatua: | Journal article |
| Hizkuntza: | English |
| Argitaratua: |
Society for Industrial and Applied Mathematics
2020
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| _version_ | 1826264782697660416 |
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| author | Hiptmair, R Jerez-Hanckes, C Urzua-Torres, C |
| author_facet | Hiptmair, R Jerez-Hanckes, C Urzua-Torres, C |
| author_sort | Hiptmair, R |
| collection | OXFORD |
| description | We consider first-kind weakly singular and hypersingular boundary integral operators for the Laplacian on screens in R3 and their Galerkin discretization by means of low-order piecewise polynomial boundary elements. For the resulting linear systems of equations we propose novel Calder´on-type preconditioners based on (i) new boundary integral operators, which provide the exact inverses of the weakly singular and hypersingular operators on flat disks, and (ii) stable duality pairings relying on dual meshes. On screens obtained as images of the unit disk under bi-Lipschitz transformations, this approach achieves condition numbers uniformly bounded in the meshwidth even on locally refined meshes. Comprehensive numerical tests also confirm its excellent pre-asymptotic performance. |
| first_indexed | 2024-03-06T20:13:23Z |
| format | Journal article |
| id | oxford-uuid:2b570de9-2a33-4f4e-8b4e-29382a625170 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:13:23Z |
| publishDate | 2020 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:2b570de9-2a33-4f4e-8b4e-29382a6251702022-03-26T12:30:16ZOptimal operator preconditioning for Galerkin boundary element methods on 3-dimensional screensJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2b570de9-2a33-4f4e-8b4e-29382a625170EnglishSymplectic Elements at OxfordSociety for Industrial and Applied Mathematics2020Hiptmair, RJerez-Hanckes, CUrzua-Torres, CWe consider first-kind weakly singular and hypersingular boundary integral operators for the Laplacian on screens in R3 and their Galerkin discretization by means of low-order piecewise polynomial boundary elements. For the resulting linear systems of equations we propose novel Calder´on-type preconditioners based on (i) new boundary integral operators, which provide the exact inverses of the weakly singular and hypersingular operators on flat disks, and (ii) stable duality pairings relying on dual meshes. On screens obtained as images of the unit disk under bi-Lipschitz transformations, this approach achieves condition numbers uniformly bounded in the meshwidth even on locally refined meshes. Comprehensive numerical tests also confirm its excellent pre-asymptotic performance. |
| spellingShingle | Hiptmair, R Jerez-Hanckes, C Urzua-Torres, C Optimal operator preconditioning for Galerkin boundary element methods on 3-dimensional screens |
| title | Optimal operator preconditioning for Galerkin boundary element methods on 3-dimensional screens |
| title_full | Optimal operator preconditioning for Galerkin boundary element methods on 3-dimensional screens |
| title_fullStr | Optimal operator preconditioning for Galerkin boundary element methods on 3-dimensional screens |
| title_full_unstemmed | Optimal operator preconditioning for Galerkin boundary element methods on 3-dimensional screens |
| title_short | Optimal operator preconditioning for Galerkin boundary element methods on 3-dimensional screens |
| title_sort | optimal operator preconditioning for galerkin boundary element methods on 3 dimensional screens |
| work_keys_str_mv | AT hiptmairr optimaloperatorpreconditioningforgalerkinboundaryelementmethodson3dimensionalscreens AT jerezhanckesc optimaloperatorpreconditioningforgalerkinboundaryelementmethodson3dimensionalscreens AT urzuatorresc optimaloperatorpreconditioningforgalerkinboundaryelementmethodson3dimensionalscreens |