On the use of rational-function fitting methods for the solution of 2D Laplace boundary-value problems
A computational scheme for solving 2D Laplace boundary-value problems using rational functions as the basis functions is described. The scheme belongs to the class of desingularized methods, for which the location of singularities and testing points is a major issue that is addressed by the proposed...
| Main Authors: | , , |
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| Format: | Article |
| Language: | en_US |
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Elsevier B.V.
2014
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| Online Access: | http://hdl.handle.net/1721.1/90970 https://orcid.org/0000-0003-1080-4005 |
| _version_ | 1826188674770927616 |
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| author | Hochman, Amit Leviatan, Yehuda White, Jacob K. |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Hochman, Amit Leviatan, Yehuda White, Jacob K. |
| author_sort | Hochman, Amit |
| collection | MIT |
| description | A computational scheme for solving 2D Laplace boundary-value problems using rational functions as the basis functions is described. The scheme belongs to the class of desingularized methods, for which the location of singularities and testing points is a major issue that is addressed by the proposed scheme, in the context he 2D Laplace equation. Well-established rational-function fitting techniques are used to set the poles, while residues are determined by enforcing the boundary conditions in the least-squares sense at the nodes of rational Gauss–Chebyshev quadrature rules. Numerical results show that errors approaching the machine epsilon can be obtained for sharp and almost sharp corners, nearly-touching boundaries, and almost-singular boundary data. We show various examples of these cases in which the method yields compact solutions, requiring fewer basis functions than the Nyström method, for the same accuracy. A scheme for solving fairly large-scale problems is also presented. |
| first_indexed | 2024-09-23T08:03:17Z |
| format | Article |
| id | mit-1721.1/90970 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T08:03:17Z |
| publishDate | 2014 |
| publisher | Elsevier B.V. |
| record_format | dspace |
| spelling | mit-1721.1/909702022-09-30T07:07:58Z On the use of rational-function fitting methods for the solution of 2D Laplace boundary-value problems Hochman, Amit Leviatan, Yehuda White, Jacob K. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Research Laboratory of Electronics Hochman, Amit White, Jacob K. A computational scheme for solving 2D Laplace boundary-value problems using rational functions as the basis functions is described. The scheme belongs to the class of desingularized methods, for which the location of singularities and testing points is a major issue that is addressed by the proposed scheme, in the context he 2D Laplace equation. Well-established rational-function fitting techniques are used to set the poles, while residues are determined by enforcing the boundary conditions in the least-squares sense at the nodes of rational Gauss–Chebyshev quadrature rules. Numerical results show that errors approaching the machine epsilon can be obtained for sharp and almost sharp corners, nearly-touching boundaries, and almost-singular boundary data. We show various examples of these cases in which the method yields compact solutions, requiring fewer basis functions than the Nyström method, for the same accuracy. A scheme for solving fairly large-scale problems is also presented. Technion, Israel Institute of Technology. Advanced Circuit Research Center Singapore-MIT Alliance Computational Engineering Programme USC Viterbi School of Engineering (Postdoctoral Fellowship) 2014-10-17T18:18:17Z 2014-10-17T18:18:17Z 2013-04 2012-06 Article http://purl.org/eprint/type/JournalArticle 00219991 http://hdl.handle.net/1721.1/90970 Hochman, Amit, Yehuda Leviatan, and Jacob K. White. “On the Use of Rational-Function Fitting Methods for the Solution of 2D Laplace Boundary-Value Problems.” Journal of Computational Physics 238 (April 2013): 337–358. https://orcid.org/0000-0003-1080-4005 en_US http://dx.doi.org/10.1016/j.jcp.2012.08.015 Journal of Computational Physics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Elsevier B.V. arXiv |
| spellingShingle | Hochman, Amit Leviatan, Yehuda White, Jacob K. On the use of rational-function fitting methods for the solution of 2D Laplace boundary-value problems |
| title | On the use of rational-function fitting methods for the solution of 2D Laplace boundary-value problems |
| title_full | On the use of rational-function fitting methods for the solution of 2D Laplace boundary-value problems |
| title_fullStr | On the use of rational-function fitting methods for the solution of 2D Laplace boundary-value problems |
| title_full_unstemmed | On the use of rational-function fitting methods for the solution of 2D Laplace boundary-value problems |
| title_short | On the use of rational-function fitting methods for the solution of 2D Laplace boundary-value problems |
| title_sort | on the use of rational function fitting methods for the solution of 2d laplace boundary value problems |
| url | http://hdl.handle.net/1721.1/90970 https://orcid.org/0000-0003-1080-4005 |
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