A Numerical Conformal Mapping Method and the Poisson Equation on Irregular Domains

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Kamgnia, Emmanuel Ricky

• Computer Science

Identifier

(UMI)AAI8409789

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/69519