Numerical solution of PDEs in periodical domains
We present in this work two schemes of approximation for numerical solutions of PDEs. The first one is the maximum entropy method (max-ent) and the second one is the b-spline method. These methods let us impose a special kind of boundary conditions: periodic boundary conditions for unbounded domains...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/113447 |
| Acceso en línea: | https://hdl.handle.net/2117/113447 |
| Access Level: | acceso abierto |
| Palabra clave: | Difference equations, Partial--Numerical solutions Max-ent B-splines Periodicity Laplace Kirchhoff plate Flexoelectricity Equacions diferencials parcials--solucions numèriques Classificació AMS::65 Numerical analysis::65N Partial differential equations, boundary value problems Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica |
| Sumario: | We present in this work two schemes of approximation for numerical solutions of PDEs. The first one is the maximum entropy method (max-ent) and the second one is the b-spline method. These methods let us impose a special kind of boundary conditions: periodic boundary conditions for unbounded domains. Some experiments need a large domain (or unbounded domain), however, this domain is divdided into some periodic cells. We develop a technique that let us simulate in the whole domain only doing a simulation in one cell. We apply this method for the resolution of second and fourth order problems (with periodic boundary conditions) like: Laplace, Kirchhoff plate and flexoelectricity. |
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