Fast and Accurate Computation of the Logarithmic Capacity of Compact Sets
| Author | Liesen, Jörg |
| Author | Sète, Olivier |
| Author | Nasser, Mohamed M. S. |
| Available date | 2020-08-27T12:05:53Z |
| Publication Date | 2017 |
| Publication Name | Computational Methods and Function Theory |
| Resource | Scopus |
| ISSN | 16179447 |
| Abstract | We 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. |
| Sponsor | We 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. |
| Language | en |
| Publisher | Springer Berlin Heidelberg |
| Subject | Boundary integral equation Cantor middle third set Chebyshev constant Conformal map Lemniscatic domain Logarithmic capacity Transfinite diameter |
| Type | Article |
| Pagination | 689-713 |
| Issue Number | 4 |
| Volume Number | 17 |
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