Parallel adaptive discontinuous Galerkin discretizations in space and time for linear elastic and acousticwaves
Dörfler, Willy
; Findeisen, Stefan; Wieners, Christian; Ziegler, Daniel
; Findeisen, Stefan; Wieners, Christian; Ziegler, DanielAbstract:
We introduce a space-time discretization for elastic and acoustic waves using a
discontinuous Galerkin approximation in space and a Petrov–Galerkin scheme in time. For the
dG method, the upwind flux is evaluated by explicitly solving a Riemann problem. Then we
show well-posedness and convergence of the discrete system. Based on goal-oriented dualweighted
error estimation an adaptive strategy is introduced. The full space-time linear system
is solved with a parallel multilevel preconditioner. Numerical experiments for acoustic and
elastic waves underline the efficiency of the overall adaptive solution process.
discontinuous Galerkin approximation in space and a Petrov–Galerkin scheme in time. For the
dG method, the upwind flux is evaluated by explicitly solving a Riemann problem. Then we
show well-posedness and convergence of the discrete system. Based on goal-oriented dualweighted
error estimation an adaptive strategy is introduced. The full space-time linear system
is solved with a parallel multilevel preconditioner. Numerical experiments for acoustic and
elastic waves underline the efficiency of the overall adaptive solution process.
| Zugehörige Institution(en) am KIT | Institut für Angewandte und Numerische Mathematik (IANM) Sonderforschungsbereich 1173 (SFB 1173) |
| Publikationstyp | Forschungsbericht/Preprint |
| Publikationsjahr | 2018 |
| Sprache | Englisch |
| Identifikator | ISSN: 2365-662X urn:nbn:de:swb:90-854422 KITopen-ID: 1000085442 |
| Verlag | Karlsruher Institut für Technologie (KIT) |
| Umfang | 29 S. |
| Serie | CRC 1173 ; 2018/14 |
| Schlagwörter | space-time methods, discontinuous Galerkin finite elements, linear hyperbolic systems, elastic and acoustic wave equation, dual weighted residual error estimator |