A domain decomposition method for approximating the conformal modules of long quadrilaterals

Abstract

This paper is concerned with the study of a domain decomposition method for approximating the conformal modules of long quadrilaterals. The method has been studied already by us and also by D. Gaier and W.K. Hayman, but only in connection with a special class of quadrilaterals, viz. quadrilaterals where: (a) the defining domain is bounded by two parallel straight lines and two Jordan arcs, and (b) the four specified boundary points are the four corners where the arcs meet the straight lines. Our main purpose here is to explain how the method may be extended to a wider class of quadrilaterals than that indicated above. © 1992 Springer-Verlag.