Time domain analysis and localization of a non-local PML for dispersive wave equations
| Autor: | Nacéra Baara, Mounir Tlemcani, Julien Diaz |
|---|---|
| Přispěvatelé: | Université des sciences et de la Technologie d'Oran Mohamed Boudiaf [Oran] (USTO MB), Modélisation et simulation de la propagation des ondes fondées sur des mesures expérimentales pour caractériser des milieux géophysiques et héliophysiques et concevoir des objets complexes (MAKUTU), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Polytechnique de Bordeaux (Bordeaux INP) |
| Rok vydání: | 2021 |
| Předmět: |
Work (thermodynamics)
Physics and Astronomy (miscellaneous) Bessel's functions long time stability symbols.namesake Convergence (routing) Applied mathematics Time domain Dispersion (water waves) Klein–Gordon equation Physics Numerical Analysis PML Applied Mathematics Zero (complex analysis) Green's function uniform error Wave equation Non local Computer Science Applications analytical solution Computational Mathematics Modeling and Simulation symbols Klein-Gordon equation dispersion [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] |
| Zdroj: | Journal of Computational Physics Journal of Computational Physics, 2021, 445, pp.110638. ⟨10.1016/j.jcp.2021.110638⟩ |
| ISSN: | 0021-9991 1090-2716 |
| DOI: | 10.1016/j.jcp.2021.110638 |
| Popis: | International audience; In this work we design and analyze new perfectly matched layers (PML) for a dispersive waves equation : the Klein Gordon equation. We show that because of the dispersion, classical PMLs do not guarantee the convergence to zero of the error, which hampers the precision in long time simulation. We propose to consider a non-local PML for which we can obtain explicit uniform estimates for the reflected analytical solution in time domain, given by an integral representation formula. This uniform estimates ensure the convergence of the error to zero at fixed time t and guarantee the accuracy of the layer. For the implementation of the new PML, we propose a localization technique that we validate numerically. |
| Databáze: | OpenAIRE |
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