The generalized finite difference method with third- and fourth-order approximations and treatment of ill-conditioned stars.
[EN]In this paper, we solve 2D and 3D second-order partial differential equations considering the Generalized Finite Difference Method with third- and fourth-order approximations. We analyze the influence of the number of points per star and establish some values as references. We propose a new stra...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad de Salamanca (USAL) |
| Repositorio: | GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| OAI Identifier: | oai:gredos.usal.es:10366/156709 |
| Acceso en línea: | http://hdl.handle.net/10366/156709 |
| Access Level: | acceso abierto |
| Palabra clave: | Generalized finite difference method Higher-order approximations Ill-conditioned stars Parallel processing 12 Matemáticas |
| Sumario: | [EN]In this paper, we solve 2D and 3D second-order partial differential equations considering the Generalized Finite Difference Method with third- and fourth-order approximations. We analyze the influence of the number of points per star and establish some values as references. We propose a new strategy to deal with ill-conditioned stars, which are frequent in higher-order approximations. This strategy uses a few points per star and presents excellent results both for detecting ill-conditioned stars and for increasing the accuracy of the numerical approximation. We apply parallel processing to the formation of stars and derivatives, and show the speedup achieved. |
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