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A numerical conformal mapping method for harmonic mixed boundary value problems

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We describe a simple and versatile technique for the numerical solution of harmonic mixed boundary value problems in simply-connected domains. This technique is based on the theory of Riemann-Hilbert problems, and involves only the use of already existing conformal mapping and quadrature routines.

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Karageorghis, A., Stylianopoulos, N.S. & Zachariades, H.A. A numerical conformal mapping method for harmonic mixed boundary value problems. J Sci Comput 11, 167–178 (1996). https://doi.org/10.1007/BF02088814

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