Numerical computation of a preimage domain for an infinite strip with rectilinear slits

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Issue Date
2023-01-16
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Authors
Kalmoun, El Mostafa
Nasser, Mohamed M. S.
Vuorinen, Matti
Advisor
Citation

Kalmoun, E.M., Nasser, M.M.S. & Vuorinen, M. Numerical computation of a preimage domain for an infinite strip with rectilinear slits. Adv Comput Math 49, 5 (2023). https://doi.org/10.1007/s10444-022-10006-y

Abstract

Let Ω be the multiply connected domain in the extended complex plane obtained by removing m non-overlapping rectilinear segments from the infinite strip . In this paper, we present an iterative method for numerical computation of a conformally equivalent bounded multiply connected domain G in the interior of the unit disk and the exterior of m non-overlapping smooth Jordan curves. We demonstrate the utility of the proposed method through two applications. First, we estimate the capacity of condensers of the form (S,E) where E ⊂ S is a union of disjoint segments. Second, we determine the streamlines associated with uniform incompressible, inviscid and irrotational flow past disjoint segments in the strip S.

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