On the numerical performance of a domain decomposition method for conformal mapping

This paper is a sequel to a recent paper [14], concerning a domain decomposition method (hereafter referred to as DDM ) for the conformal mapping of a certain class of quadrilaterals. For the description of the DDM we proceed exactly as in [14:§1], by introducing the following terminology and notations

A domain decomposition method for conformal mapping onto a rectangle

Let g be the function which maps conformally a simply-connected domain G onto a rectangle R so that four specified points z1, z2, z3, z4,o n ∂G are mapped respectively onto the four vertices of R. This paper is concerned with the study of a domain decomposition method for computing approximations to g and to an associated domain functional in cases where: (i) G is bounded by two parallel straight lines and two Jordan arcs. (ii) The four points z1, z2, z3, z4, are the corners where the two straight lines meet the two arcs

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

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 qua-drilaterals than that indicated above

A numerical method for the computation of faber polynomials for starlike domains

We describe a simple numerical process (based on the Theodorsen method for conformal mapping ) for computing approximations to Faber polynomials for starlike domains