4 research outputs found
Approximating the conformal map of elongated quadrilaterals by domain decomposition
Let be a quadrilateral consisting of a Jordan domain and four points , , ,
in counterclockwise order on and let be the conformal module of . Then, is conformally equivalent to the rectangular quadrilateral ,
where in the sense that there exists a unique conformal map that takes the four points , ,
, , respectively onto the four vertices , , , of . In this paper we consider the use of a domain decomposition method (DDM) for computing approximations to the conformal map , in cases where the quadrilateral is "long". The method has been studied already but, mainly, in connection with the computation of . Here we consider certain recent results of Laugesen, for the DDM approximation of the conformal map associated with a special class of quadrilaterals (viz. quadrilaterals whose two non-adjacent boundary segments and are parallel straight lines) and seek to extend these results to more general quadrilaterals. By making use of the available DDM theory for conformal modules, we show that the corresponding theory for can, indeed, be extended to a much wider class of quadrilaterals than those considered by Laugesen
Curvilinear crosscuts of subdivision for a domain decomposition method in numerical conformal mapping
Let be a quadrilateral consisting of a Jordan domain and four distinct points
, , and in counterclockwise order on . We consider a domain decomposition method
for computing approximations to the conformal module of in cases where is "long'' or, equivalently,
is "large''. This method is based on decomposing the original quadrilateral into two or more component
quadrilaterals , and then approximating by the sum of the the modules of the component
quadrilaterals. The purpose of this paper is to consider ways for determining appropriate crosscuts of subdivision and, in particular, to show that there are cases where the use of curved crosscuts is much more appropriate than the straight line crosscuts that have been used so far
A domain decomposition method for numerical conformal mapping onto a rectangle
SIGLEAvailable from British Library Document Supply Centre- DSC:DX92574 / BLDSC - British Library Document Supply CentreGBUnited Kingdo