Fully implicit and semi-implicit hybrid discontinuous space-time Galerkin methods for acoustic wave propagation
Abstract/Contents
- Abstract
- This dissertation, based on the concept of the existing discontinuous Enrichment method (DEM) for frequency domain analysis, proposes a hybrid discontinuous Galerkin method (DGM) for the numerical solution of transient problems governed by the wave equation in two and three spatial dimensions. This hybrid DGM extends concepts of DEM into the time domain for problems that are better suited for analysis in time domain. The discontinuous formulation in both space and time enables the use of solutions to the homogeneous wave equation in the approximation. In this dissertation, within each finite element, the solutions in the form of polynomial waves are employed. The continuity of these polynomial waves is weakly enforced through suitably chosen Lagrange multipliers. Numerical results for two and three dimensional model problems, in both low and mid frequency regimes, show that the proposed DGM outperforms the conventional space-time finite element method and Newmark family semi-discrete schemes. Additionally an alternative semi-implicit formulation is proposed where global level linear systems stemming from the implicit formulation is traded in favour of smaller and independent local systems. Numerical results for two dimensional model problems, in both low and mid frequency regimes, show that for a fixed mesh resolution, the semi-implicit DGM requires far less memory than its fully implicit counterpart. The semi-implicit scheme also parallelizes and scales very well with the number of available CPUs.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2014 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Wang, Dalei |
|---|---|
| Associated with | Stanford University, Institute for Computational and Mathematical Engineering. |
| Primary advisor | Farhat, Charbel |
| Thesis advisor | Farhat, Charbel |
| Thesis advisor | Lew, Adrian |
| Thesis advisor | Papanicolaou, George |
| Advisor | Lew, Adrian |
| Advisor | Papanicolaou, George |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Dalei Wang. |
|---|---|
| Note | Submitted to the Institute for Computational and Mathematical Engineering. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2014. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2014 by Dalei Wang
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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