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....

Full description

Saved in:
Bibliographic Details
Published in:Journal of computational methods in applied mathematics Vol. 19; no. 3; pp. 465 - 481
Main Authors: Ernesti, Johannes, Wieners, Christian
Format: Journal Article
Language:English
Published: Minsk De Gruyter 01.07.2019
Walter de Gruyter GmbH
Subjects:
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
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1609-4840
1609-9389
DOI:10.1515/cmam-2018-0190