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

Abstract

Summary. 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. Mathematics Subject Classification (1991): 30C30, 65E05

A Nonoverlapping Domain Decomposition Method for Symm's Equation for Conformal Mapping

“…There has been little study of domain decomposition in conformal mapping [6,9,20,21] and apparently none relating to integral equations for conformal mapping. This is true despite the fact that Symm's method is essentially an indirect boundary element method for Laplace's equation, and domain decomposition is common in boundary element methods generally [4,16].…”