Conformal mapping of polygonal domains

Analysis and design of polygonal resistors by conformal mapping

To compute the electrical resistance ( ~ conformal modulus) of a polygonally shaped resistorcut from a sheet of uniform resistivity, it suffices to find a conformal map of the polygon onto arectangle. Constructing such a map requires the solution of a Schwarz-Christoffel parameter prob-lem. First we show by examples that this is practical numerically. Then we consider an inverse 704...

Conformal Mapping of Long Quadrilaterals and Thick Doubly Connected Domains

Abstract. In this paper we investigate theoretically an approximation technique for avoiding the crowding phenomenon in numerical conformal mapping. The method applies to conformal maps from rectangles to "long quadrilaterals," i.e., Jordan domains bounded by two parallel straight lines and two Jordan arcs, where the two arcs are far apart. We require that these maps take the four corners of th...

A General Theorem on Conformal Mapping of Multiply Connected Domains.

Green's Functions for Multiply Connected Domains via Conformal Mapping

A method is described for the computation of the Green’s function in the complex plane corresponding to a set of K symmetrically placed polygons along the real axis. An important special case is a set of K real intervals. The method is based on a Schwarz–Christoffel conformal map of the part of the upper half-plane exterior to the problem domain onto a semi-infinite strip whose end contains K −...

Homogenization in polygonal domains

We consider the homogenization of elliptic systems with ε-periodic coefficients. Classical two-scale approximation yields a O(ε) error inside the domain. We discuss here the existence of higher order corrections, in the case of general polygonal domains. The corrector depends in a non-trivial way on the boundary. Our analysis extends substantially previous results obtained for polygonal domains...