Using HDG+ to Compute Solutions of the 3D Linear Elastic and Poroelastic Wave Equations
| Author(s) | Hungria, Allan | |
| Date Accessioned | 2020-02-21T12:52:05Z | |
| Date Available | 2020-02-21T12:52:05Z | |
| Publication Date | 2019 | |
| SWORD Update | 2020-02-03T13:26:49Z | |
| Abstract | We are interested in the numerical simulation of elastic and poroelastic waves in three dimensions on polyhedral domains. First we tackle the frequency-domain case for elasticity, proving that our HDG+ method's solution converges at O(h^{k+2}) to the exact displacement solution and O(h^{k+1}) to the exact stress solution, where k is the polynomial degree used in the approximation and h is the maximum length of an edge of our tetrahedra. Next we show numerical experiments to verify these results. We then extend our results to the time-domain, proving that the system is conservative and showing numerical results that match our predictions. Then we introduce an extended method by adding a third variable corresponding to the strain, and show numerical results that match our predictions. We next go on to explore HDG+ for Biot's poroelastic system in 3D, proving dissipativity of our method and showing numerical results of the same convergence rates as well as O(h^{k+2}) for pressure and O(h^{k+1}) for pressure flux in both the frequency domain and the time-domain. | en_US |
| Advisor | Sayas, Francisco-Javier | |
| Degree | Ph.D. | |
| Department | University of Delaware, Department of Mathematical Sciences | |
| DOI | https://doi.org/10.58088/ga63-d156 | |
| Unique Identifier | 1141251886 | |
| URL | http://udspace.udel.edu/handle/19716/25044 | |
| Language | en | |
| Publisher | University of Delaware | en_US |
| URI | https://search.proquest.com/docview/2307785099?accountid=10457 | |
| Title | Using HDG+ to Compute Solutions of the 3D Linear Elastic and Poroelastic Wave Equations | en_US |
| Type | Thesis | en_US |