A numerical conformal mapping method and the poisson equation on irregular domains
Emmanuel Kamgnia · 1984
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.