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

Subject Area

Mathematics, Applied

Number of Pages

88

Format

.pdf

Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License

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