Displaying similar documents to “Theoretical scheme on numerical conformal mapping of unbounded multiply connected domain by fundamental solutions method.”

Conformal mapping of the domain bounded by a circular polygon with zero angles onto the unit disc

Vladimir Mityushev (1998)

Annales Polonici Mathematici

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The conformal mapping ω(z) of a domain D onto the unit disc must satisfy the condition |ω(t)| = 1 on ∂D, the boundary of D. The last condition can be considered as a Dirichlet problem for the domain D. In the present paper this problem is reduced to a system of functional equations when ∂D is a circular polygon with zero angles. The mapping is given in terms of a Poincaré series.

Conformal mapping and inverse conductivity problem with one measurement

Marc Dambrine, Djalil Kateb (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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This work deals with a two-dimensional inverse problem in the field of tomography. The geometry of an unknown inclusion has to be reconstructed from boundary measurements. In this paper, we extend previous results of R. Kress and his coauthors: the leading idea is to use the conformal mapping function as unknown. We establish an integrodifferential equation that the trace of the Riemann map solves. We write it as a fixed point equation and give conditions for contraction. We conclude...