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AuthorLiesen, Jörg
AuthorSète, Olivier
AuthorNasser, Mohamed M. S.
Available date2020-08-27T12:05:53Z
Publication Date2017
Publication NameComputational Methods and Function Theory
ResourceScopus
ISSN16179447
URIhttp://dx.doi.org/10.1007/s40315-017-0207-1
URIhttp://hdl.handle.net/10576/15853
AbstractWe 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.
SponsorWe 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.
Languageen
PublisherSpringer Berlin Heidelberg
SubjectBoundary integral equation
Cantor middle third set
Chebyshev constant
Conformal map
Lemniscatic domain
Logarithmic capacity
Transfinite diameter
TitleFast and Accurate Computation of the Logarithmic Capacity of Compact Sets
TypeArticle
Pagination689-713
Issue Number4
Volume Number17
dc.accessType Abstract Only


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