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Fast and Accurate Computation of the Logarithmic Capacity of Compact Sets

المؤلفLiesen, Jörg
المؤلفSète, Olivier
المؤلفNasser, Mohamed M. S.
تاريخ الإتاحة2020-08-27T12:05:53Z
تاريخ النشر2017
اسم المنشورComputational Methods and Function Theory
المصدرScopus
الرقم المعياري الدولي للكتاب16179447
معرّف المصادر الموحدhttp://dx.doi.org/10.1007/s40315-017-0207-1
معرّف المصادر الموحدhttp://hdl.handle.net/10576/15853
الملخصWe present a numerical method for computing the logarithmic capacity of compact subsets of C, which are bounded by Jordan curves and have finitely connected complement. The subsets may have several components and need not have any special symmetry. The method relies on the conformal map onto lemniscatic domains and, computationally, on the solution of a boundary integral equation with the Neumann kernel. Our numerical examples indicate that the method is fast and accurate. We apply it to give an estimate of the logarithmic capacity of the Cantor middle third set and generalizations of it. - 2017, Springer-Verlag Berlin Heidelberg.
راعي المشروعWe thank Thomas Ransford for bringing to our attention the analytic formula for the capacity of two unequal disks (Example 4.7). We also thank Nick Trefethen for sharing the numerical results on the capacity of the Cantor middle third set he obtained together with Banjai and Embree.
اللغةen
الناشرSpringer Berlin Heidelberg
الموضوعBoundary integral equation
Cantor middle third set
Chebyshev constant
Conformal map
Lemniscatic domain
Logarithmic capacity
Transfinite diameter
العنوانFast and Accurate Computation of the Logarithmic Capacity of Compact Sets
النوعArticle
الصفحات689-713
رقم العدد4
رقم المجلد17


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