Abstract
Numerical methods have been developed to solve partial differential equations involving the far-field radiation of waves. In addition, there has been recent interest in uncertainty quantification- a burgeoning field involving solving PDEs where random variables are used to model uncertainty in the data. In this thesis we will apply uncertainty quantification methodology to the 1D and 2D wave equation with nonreflecting boundary. We first derive a boundary condition for the 1D wave equation assuming several models of the random wave speed. Later we use our result to compare to an asymptotic SDE approach, and finally we repeat our analysis for the 2D wave equation, providing numerical results for each.
Degree Date
Fall 12-19-2020
Document Type
Dissertation
Degree Name
Ph.D.
Department
Mathematics
Advisor
Thomas Hagstrom
Second Advisor
Andrea Barreiro
Third Advisor
Wei Cai
Fourth Advisor
Mohammad Motamed
Fifth Advisor
Minh-Binh Tran
Number of Pages
88
Format
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License
Recommended Citation
Citty, Brian, "Uncertainty Quantification of Nonreflecting Boundary Schemes" (2020). Mathematics Theses and Dissertations. 12.
https://scholar.smu.edu/hum_sci_mathematics_etds/12
