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Numerical computation of a preimage domain for an infinite strip with rectilinear slits
Kalmoun, El Mostafa Nasser, Mohamed M. S. Vuorinen, Matti
Kalmoun, El Mostafa
Nasser, Mohamed M. S.
Vuorinen, Matti
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2023-01-16
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Numerical conformal mappings,Condenser capacity,Conformal invariance,Boundary integral equation
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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 $\overline {\mathbb {C}}$obtained by removing m non-overlapping rectilinear segments from the infinite strip $S=\{z : \left |\text {Im} z\right |<\pi /2\}$. 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 $\mathbb {D}$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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Preprint version available from arXiv. Click on the DOI to access the publisher's version of this article.
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Advances in Computational Mathematics
Volume 49, No. 1
Volume 49, No. 1
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1572-9044