Abstract
We discuss how the Fast Multipole Method (FMM) applied to a boundary concentrated mesh can be used to evaluate volume potentials that arise in the boundary element method. If $h$ is the meshwidth near the boundary, then the algorithm can compute the potential in nearly $\Ord(h^{-2})$ operations while maintaining an $\Ord(h^p)$ convergence of the error. The effectiveness of the algorithms are demonstrated by solving boundary integral equations of the Poisson equation.
Degree Date
Summer 8-4-2021
Document Type
Dissertation
Degree Name
Ph.D.
Department
Mathematics
Advisor
Dr. Johannes Tausch
Subject Area
Computer Engineering, Computer Science
Number of Pages
93
Format
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License
Recommended Citation
Mohyaddin, Sasan, "A Fast Method For Computing Volume Potentials In The Galerkin Boundary Element Method In 3D Geometries" (2021). Mathematics Theses and Dissertations. 14.
https://scholar.smu.edu/hum_sci_mathematics_etds/14
Included in
Numerical Analysis and Computation Commons, Numerical Analysis and Scientific Computing Commons, Other Physical Sciences and Mathematics Commons
