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Construction of complex potentials for multiply connected domain

Ivanshin Pyotr N.

Journal of Applied Analysis

2021

Vol. 27, nr 2

209--217

The method of reduction of a Fredholm integral equation to the linear system is generalized to construction of a complex potential - an analytic function in an unbounded multiply connected domain with a simple pole at infinity which maps the domain onto a plane with horizontal slits. We consider a locally sourceless, locally irrotational flow on an arbitrary given n-connected unbounded domain with impermeable boundary. The complex potential has the form of a Cauchy integral with one linear and n logarithmic summands. The method is easily computable.

On approximate conformal mapping of a disk and an annulus with radial and circular slits onto multiply connected domains

Ivanshin Pyotr N., Shirokova Elena A.

Journal of Applied Mathematics and Computational Mechanics

2020

Vol. 19, nr 2

73--84

The method of boundary curve reparametrization is generalized to the case of multiply connected domains. We construct the approximate analytical conformal mapping of the unit disk with m circular slits and n-m radial slits and an annulus with (m-1) circular slits and n-m radial slits onto an arbitrary given (n+1) multiply connected finite domain with a smooth boundary. The method is based on extension of the Lichtenstein-Gershgorin equation to a multiply connected domain. The proposed method is reduced to the solution of a linear system with unknown Fourier coefficients. The approximate mapping function has the form of a Cauchy integral. Numerical examples demonstrate that the proposed method is effective in computations.