CALCULUS ON SURFACES WITH GENERAL CLOSEST POINT FUNCTIONS
The closest point method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys., 227 (2008), pp. 1943- 1961] and successfully applied to a variety of surface PDEs. In this paper we study the theoretical foundations of this...
| Główni autorzy: | , |
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| Format: | Journal article |
| Język: | English |
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2012
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| _version_ | 1826281528850644992 |
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| author | Maerz, T Macdonald, C |
| author_facet | Maerz, T Macdonald, C |
| author_sort | Maerz, T |
| collection | OXFORD |
| description | The closest point method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys., 227 (2008), pp. 1943- 1961] and successfully applied to a variety of surface PDEs. In this paper we study the theoretical foundations of this method. The main idea is that surface differentials of a surface function can be replaced with Cartesian differentials of its closest point extension, i.e., its composition with a closest point function. We introduce a general class of these closest point functions (a subset of differentiable retractions), show that these are exactly the functions necessary to satisfy the above idea, and give a geometric characterization of this class. Finally, we construct some closest point functions and demonstrate their effectiveness numerically on surface PDEs. © 2012 Society for Industrial and Applied Mathematics. |
| first_indexed | 2024-03-07T00:30:10Z |
| format | Journal article |
| id | oxford-uuid:7f7f11cb-5ccc-4e46-97ac-cfe4a2adf555 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:30:10Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:7f7f11cb-5ccc-4e46-97ac-cfe4a2adf5552022-03-26T21:17:17ZCALCULUS ON SURFACES WITH GENERAL CLOSEST POINT FUNCTIONSJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7f7f11cb-5ccc-4e46-97ac-cfe4a2adf555EnglishSymplectic Elements at Oxford2012Maerz, TMacdonald, CThe closest point method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys., 227 (2008), pp. 1943- 1961] and successfully applied to a variety of surface PDEs. In this paper we study the theoretical foundations of this method. The main idea is that surface differentials of a surface function can be replaced with Cartesian differentials of its closest point extension, i.e., its composition with a closest point function. We introduce a general class of these closest point functions (a subset of differentiable retractions), show that these are exactly the functions necessary to satisfy the above idea, and give a geometric characterization of this class. Finally, we construct some closest point functions and demonstrate their effectiveness numerically on surface PDEs. © 2012 Society for Industrial and Applied Mathematics. |
| spellingShingle | Maerz, T Macdonald, C CALCULUS ON SURFACES WITH GENERAL CLOSEST POINT FUNCTIONS |
| title | CALCULUS ON SURFACES WITH GENERAL CLOSEST POINT FUNCTIONS |
| title_full | CALCULUS ON SURFACES WITH GENERAL CLOSEST POINT FUNCTIONS |
| title_fullStr | CALCULUS ON SURFACES WITH GENERAL CLOSEST POINT FUNCTIONS |
| title_full_unstemmed | CALCULUS ON SURFACES WITH GENERAL CLOSEST POINT FUNCTIONS |
| title_short | CALCULUS ON SURFACES WITH GENERAL CLOSEST POINT FUNCTIONS |
| title_sort | calculus on surfaces with general closest point functions |
| work_keys_str_mv | AT maerzt calculusonsurfaceswithgeneralclosestpointfunctions AT macdonaldc calculusonsurfaceswithgeneralclosestpointfunctions |