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

202 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 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.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD