Fast computing of conformal mapping and its inverse of bounded multiply connected regions onto second, third and fourth categories of Koebe's canonical slit regions (Q333218)

A boundary integral method was presented in [the first author et al., ``Spiral slits map and its inverse of bounded multiply connected regions'', Appl. Math. Comput. 228, 520--530 (2014; Zbl 1364.30014); ``Annulus with spiral slits map and its inverse of bounded multiply connected regions'', Int. J. Sci. Eng. Res 4, No. 10, 1447--1454 (2013)] for conformal mappings of a bounded multiply connected region onto certain slit regions. In the present paper, the authors extend this method to maps onto disks with spiral slits. The proposed method is based on a unique boundary integral equation with adjoint generalized Neumann kernel. A fast and effective numerical implementation of the method is also presented. The integral equations are solved numerically, using a combination of the Nystrøm method, the GMRES method, and the fast multipole method (FMM). Further, the numerical results of some test calculations are presented, which illustrate that the method of the authors is able to handle regions with very high connectivity.