On perfectly matched layers for discontinuous Petrov–Galerkin methods

In this article, several discontinuous Petrov–Galerkin (DPG) methods with perfectly matched layers (PMLs) are derived along with their quasi-optimal graph test norms. Ultimately, two different complex coordinate stretching strategies are considered in these derivations. Unlike with classical formula...

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Bibliographic Details
Published in:Computational mechanics 2019-06, Vol.63 (6), p.1131-1145
Main Authors: Vaziri Astaneh, Ali, Keith, Brendan, Demkowicz, Leszek
Format: Article
Language:English
Subjects:
Acoustic propagation
Analysis
Classical and Continuum Physics
Computational Science and Engineering
Domains
Electric waves
Electromagnetic radiation
Electromagnetic waves
Electromagnetism
Engineering
Formulations
Galerkin method
Mathematical analysis
Methods
Norms
Original Paper
Perfectly matched layers
Theoretical and Applied Mechanics
Wave propagation
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Summary:In this article, several discontinuous Petrov–Galerkin (DPG) methods with perfectly matched layers (PMLs) are derived along with their quasi-optimal graph test norms. Ultimately, two different complex coordinate stretching strategies are considered in these derivations. Unlike with classical formulations used by Bubnov–Galerkin methods, with so-called ultraweak variational formulations, these two strategies in fact deliver different formulations in the PML region. One of the strategies, which is argued to be more physically natural, is employed for numerically solving two- and three-dimensional time-harmonic acoustic, elastic, and electromagnetic wave propagation problems, defined in unbounded domains. Through these numerical experiments, efficacy of the new DPG methods with PMLs is verified.
ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-018-1640-3