Conformal Mappings with Applications to Computational Geometry

Abstract

Conformal mapping is extremely important in complex analysis as well as in many areas of physics and engineering. Our main goal in this thesis is to present a successful application of conformal transformations in solving boundary value problems. conformal transformation has been used to generate orthogonal curvilinear coordinates for solving various problems in simply connected regions. Consequently, if one is solving an elliptic boundary value problem, an appropriate conformal mapping could be used simultaneously to fit the boundary curves with coordinate lines and simplify the original partial differential equation.