Green's functions for multiply connected domains via conformal mapping
A method is described for the computation of the Green's function in the complex plane corresponding to a set of K symmetrically placed polygons along the real axis. An important special case is a set of K real intervals. The method is based on a Schwarz-Christoffel conformal map of the part of...
| Main Authors: | , |
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| Format: | Report |
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SIAM
1998
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| _version_ | 1797078490796785664 |
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| author | Embree, M Trefethen, L |
| author_facet | Embree, M Trefethen, L |
| author_sort | Embree, M |
| collection | OXFORD |
| description | A method is described for the computation of the Green's function in the complex plane corresponding to a set of K symmetrically placed polygons along the real axis. An important special case is a set of K real intervals. The method is based on a Schwarz-Christoffel conformal map of the part of the upper half-plane exterior to the problem domain onto a semi-infinite strip whose end contains K-1 slits. From the Green's function one can obtain a great deal of information about polynomial approximations, with applications in digital filters and matrix iteration. By making the end of the strip jagged, the method can be generalised to weighted Green's functions and weighted approximations. |
| first_indexed | 2024-03-07T00:32:37Z |
| format | Report |
| id | oxford-uuid:805711fd-ba09-4147-ac11-24a7975f0b6c |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:32:37Z |
| publishDate | 1998 |
| publisher | SIAM |
| record_format | dspace |
| spelling | oxford-uuid:805711fd-ba09-4147-ac11-24a7975f0b6c2022-03-26T21:22:37ZGreen's functions for multiply connected domains via conformal mappingReporthttp://purl.org/coar/resource_type/c_93fcuuid:805711fd-ba09-4147-ac11-24a7975f0b6cMathematical Institute - ePrintsSIAM1998Embree, MTrefethen, LA method is described for the computation of the Green's function in the complex plane corresponding to a set of K symmetrically placed polygons along the real axis. An important special case is a set of K real intervals. The method is based on a Schwarz-Christoffel conformal map of the part of the upper half-plane exterior to the problem domain onto a semi-infinite strip whose end contains K-1 slits. From the Green's function one can obtain a great deal of information about polynomial approximations, with applications in digital filters and matrix iteration. By making the end of the strip jagged, the method can be generalised to weighted Green's functions and weighted approximations. |
| spellingShingle | Embree, M Trefethen, L Green's functions for multiply connected domains via conformal mapping |
| title | Green's functions for multiply connected domains via conformal mapping |
| title_full | Green's functions for multiply connected domains via conformal mapping |
| title_fullStr | Green's functions for multiply connected domains via conformal mapping |
| title_full_unstemmed | Green's functions for multiply connected domains via conformal mapping |
| title_short | Green's functions for multiply connected domains via conformal mapping |
| title_sort | green s functions for multiply connected domains via conformal mapping |
| work_keys_str_mv | AT embreem greensfunctionsformultiplyconnecteddomainsviaconformalmapping AT trefethenl greensfunctionsformultiplyconnecteddomainsviaconformalmapping |