Theses and Dissertations
Issuing Body
Mississippi State University
Advisor
Bhatia, Manav
Committee Member
Richardson, Joseph D.
Committee Member
Hamilton, Michael D.
Committee Member
Hensley, Jeffrey L.
Date of Degree
8-9-2019
Document Type
Dissertation - Open Access
Major
Computational Engineering
Degree Name
Doctor of Philosophy
College
James Worth Bagley College of Engineering
Department
Computational Engineering Program
Abstract
The present work presents a number of contributions to the areas of numerical integration, singular integrals, and boundary element methods. The first contribution is an elemental distortion technique, based on the Duffy transformation, used to improve efficiency for the numerical integration of near hypersingular integrals. Results show that this method can reduce quadrature expense by up to 75 percent over the standard Duffy transformation. The second contribution is an improvement to integration of weakly singular integrals by using regularization to smooth weakly singular integrals. Errors show that the method may reduce errors by several orders of magnitude for the same quadrature order. The final work investigated the use of regularization applied to hypersingular integrals in the context of the boundary element method in three dimensions. This work showed that by using the simple solutions technique, the BEM is reduced to a weakly singular form which directly supports numerical integration. Results support that the method is more efficient than the state-of-the-art.
URI
https://hdl.handle.net/11668/14486
Recommended Citation
Marshall, Joshua P., "High Order Implementation in Integral Equations" (2019). Theses and Dissertations. 2490.
https://scholarsjunction.msstate.edu/td/2490