Dissertation/Thesis Abstract

Using HDG+ to Compute Solutions of the 3D Linear Elastic and Poroelastic Wave Equations
by Hungria, Allan, Ph.D., University of Delaware, 2019, 139; 22588757
Abstract (Summary)

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(hk + 2) to the exact displacement solution and O(hk + 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(hk + 2) for pressure and O(hk + 1) for pressure flux in both the frequency domain and the time-domain.

Indexing (document details)
Advisor: Sayas, Francisco-Javier
Commitee: Monk, Peter, Bacuta, Constantin, Cockburn, Bernardo
School: University of Delaware
Department: Mathematical Sciences
School Location: United States -- Delaware
Source: DAI-B 81/4(E), Dissertation Abstracts International
Source Type: DISSERTATION
Subjects: Applied Mathematics, Materials science, Mechanics
Keywords: Elasticity, HDG, HDG+, Poroelasticity
Publication Number: 22588757
ISBN: 9781687974228
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