Space-Time Discontinuous Petrov–Galerkin Methods for Linear Wave Equations in Heterogeneous Media

We establish an abstract space-time DPG framework for the approximation of linear waves in heterogeneous media. The estimates are based on a suitable variational setting in the energy space. The analysis combines the approaches for acoustic waves of Gopalakrishnan–Sepulveda [J. Gopalakrishnan and P....

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Vydáno v:Journal of computational methods in applied mathematics Ročník 19; číslo 3; s. 465 - 481
Hlavní autoři: Ernesti, Johannes, Wieners, Christian
Médium: Journal Article
Jazyk:angličtina
Vydáno: Minsk De Gruyter 01.07.2019
Walter de Gruyter GmbH
Témata:
65M15
65M55
65M60
Acoustic waves
Discontinuous Petrov–Galerkin Finite Elements
Galerkin method
Heterogenous Media
Linear Hyperbolic Systems
Mathematical analysis
Partial differential equations
Space-Time Methods
Spacetime
Wave equations
ISSN:1609-4840, 1609-9389
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Shrnutí:We establish an abstract space-time DPG framework for the approximation of linear waves in heterogeneous media. The estimates are based on a suitable variational setting in the energy space. The analysis combines the approaches for acoustic waves of Gopalakrishnan–Sepulveda [J. Gopalakrishnan and P. Sepulveda, A space-time DPG method for the wave equation in multiple dimensions, Space-Time Methods. Applications to Partial Differential Equations, Radon Ser. Comput. Appl. Math. 21, Walter de Gruyter, Berlin 2019, 129–154] and Ernesti–Wieners [J. Ernesti and C. Wieners, A space-time discontinuous Petrov–Galerkin method for acoustic waves, Space-Time Methods. Applications to Partial Differential Equations, Radon Ser. Comput. Appl. Math. 21, Walter de Gruyter, Berlin 2019, 99–127] and is based on the abstract definition of traces on the skeleton of the time-space substructuring. The method is evaluated by large-scale parallel computations motivated from applications in seismic imaging, where the computational domain can be restricted substantially to a subset of the full space-time cylinder.
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ISSN:1609-4840
1609-9389
DOI:10.1515/cmam-2018-0190