A Numerical Conformal Mapping Method and the Poisson Equation on Irregular Domains
Kamgnia, Emmanuel Ricky
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Permalink
https://hdl.handle.net/2142/69519
Description
Title
A Numerical Conformal Mapping Method and the Poisson Equation on Irregular Domains
Author(s)
Kamgnia, Emmanuel Ricky
Issue Date
1984
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Computer Science
Abstract
In this thesis, we propose a numerical conformal mapping procedure for constructing the unique transformation that maps a unit disk onto a simply connected irregular region. All the systems of linear equations that arise in formulating the method, are solved using Rapid Elliptic Solvers. Therefore, this technique may be regarded as a fast mapping technique. Applications of the method include: (i) generation curvilinear coordinate systems, and (ii) solving the Poisson and Laplace equations on two-dimensional simply connected irregular domains.
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