Closed-form inverses of the weakly singular and hypersingular operators on disks
We introduce new boundary integral operators which are the exact inverses of the weakly singular and hypersingular operators for the Laplacian on flat disks. Moreover, we provide explicit closed forms for them and prove the continuity and ellipticity of their corresponding bilinear forms in the natu...
| Autores principales: | , , |
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| Formato: | Journal article |
| Lenguaje: | English |
| Publicado: |
Springer Verlag
2018
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| _version_ | 1826280545981562880 |
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| author | Hiptmair, R Jerez-Hanckes, C Urzúa-Torres, C |
| author_facet | Hiptmair, R Jerez-Hanckes, C Urzúa-Torres, C |
| author_sort | Hiptmair, R |
| collection | OXFORD |
| description | We introduce new boundary integral operators which are the exact inverses of the weakly singular and hypersingular operators for the Laplacian on flat disks. Moreover, we provide explicit closed forms for them and prove the continuity and ellipticity of their corresponding bilinear forms in the natural Sobolev trace spaces. This permit us to derive new Calder\'on-type identities that can provide the foundation for optimal operator preconditioning in Galerkin boundary element methods. |
| first_indexed | 2024-03-07T00:15:18Z |
| format | Journal article |
| id | oxford-uuid:7aa28b1c-2de6-47e9-a874-ebf36862b40b |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:15:18Z |
| publishDate | 2018 |
| publisher | Springer Verlag |
| record_format | dspace |
| spelling | oxford-uuid:7aa28b1c-2de6-47e9-a874-ebf36862b40b2022-03-26T20:45:16ZClosed-form inverses of the weakly singular and hypersingular operators on disksJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7aa28b1c-2de6-47e9-a874-ebf36862b40bEnglishSymplectic Elements at OxfordSpringer Verlag2018Hiptmair, RJerez-Hanckes, CUrzúa-Torres, CWe introduce new boundary integral operators which are the exact inverses of the weakly singular and hypersingular operators for the Laplacian on flat disks. Moreover, we provide explicit closed forms for them and prove the continuity and ellipticity of their corresponding bilinear forms in the natural Sobolev trace spaces. This permit us to derive new Calder\'on-type identities that can provide the foundation for optimal operator preconditioning in Galerkin boundary element methods. |
| spellingShingle | Hiptmair, R Jerez-Hanckes, C Urzúa-Torres, C Closed-form inverses of the weakly singular and hypersingular operators on disks |
| title | Closed-form inverses of the weakly singular and hypersingular operators on disks |
| title_full | Closed-form inverses of the weakly singular and hypersingular operators on disks |
| title_fullStr | Closed-form inverses of the weakly singular and hypersingular operators on disks |
| title_full_unstemmed | Closed-form inverses of the weakly singular and hypersingular operators on disks |
| title_short | Closed-form inverses of the weakly singular and hypersingular operators on disks |
| title_sort | closed form inverses of the weakly singular and hypersingular operators on disks |
| work_keys_str_mv | AT hiptmairr closedforminversesoftheweaklysingularandhypersingularoperatorsondisks AT jerezhanckesc closedforminversesoftheweaklysingularandhypersingularoperatorsondisks AT urzuatorresc closedforminversesoftheweaklysingularandhypersingularoperatorsondisks |