MESH GENERATION BY CONFORMAL AND QUASICONFORMAL MAPPINGS

Abstract

This chapter describes the mesh generation by conformal and quasiconformal mappings. Advances in the finite-difference solution of elliptic equations have been limited to regions whose boundary contours coincide with the coordinate lines of the Cartesian coordinate system. The reason for this lies in the fact that when an arbitrary curvilinear coordinate system is used, the original equation becomes much more complex. Poisson's equation is transformed to an equation with variable coefficients and a mixed derivative term. There is no added complexity, or additional computer storage needed for the coefficients, if an orthogonal coordinate system is generated from a conformal mapping. Quasiconformal mappings were initially conceived to reduce any second order linear elliptic partial differential equation to canonical form. The mapping parameters are determined from the boundary correspondence and the method of Mastin and Thompson would be difficult to implement on arbitrary regions.