Constructing Multiply Connected Quadrature Domains
Darren Crowdy, Jonathan S. Marshall · SIAM Journal on Applied Mathematics · 2004
Multiply connected bounded quadrature domains, with finite connectivity, are reconstructed from their quadrature data using conformal mappings that are ratios of products of Schottky--Klein prime functions. This method provides the natural generalization of the conformal maps to simply and doubly connected quadrature domains constructed by the first author in a number of physical applications. The efficacy of the method is demonstrated by the explicit construction of a range of examples as well as by comparison with alternative constructive methods recently introduced by Crowdy [R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 457 (2001), pp. 2337--2359] and Richardson [European J. Appl. Math., 12 (2001), pp. 571--599].