Fast and Accurate Computation of the Logarithmic Capacity of Compact Sets
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 lemnis...
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| Veröffentlicht in: | Computational methods and function theory 2017-12, Vol.17 (4), p.689-713 |
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| container_title | Computational methods and function theory |
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| creator | Liesen, Jörg Sète, Olivier Nasser, Mohamed M. S. |
| description | 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. |
| doi_str_mv | 10.1007/s40315-017-0207-1 |
| format | Article |
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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.</description><identifier>ISSN: 1617-9447</identifier><identifier>EISSN: 2195-3724</identifier><identifier>DOI: 10.1007/s40315-017-0207-1</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Analysis ; Computational Mathematics and Numerical Analysis ; Conformal mapping ; Functions of a Complex Variable ; Integral equations ; Mathematics ; Mathematics and Statistics ; Numerical analysis</subject><ispartof>Computational methods and function theory, 2017-12, Vol.17 (4), p.689-713</ispartof><rights>Springer-Verlag Berlin Heidelberg 2017</rights><rights>Copyright Springer Science & Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-e415c7c4fcdf26c1f576b6f954abf46133aeed6e8ac2e3d6f10d4c6d995adcf33</citedby><cites>FETCH-LOGICAL-c316t-e415c7c4fcdf26c1f576b6f954abf46133aeed6e8ac2e3d6f10d4c6d995adcf33</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s40315-017-0207-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40315-017-0207-1$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Liesen, Jörg</creatorcontrib><creatorcontrib>Sète, Olivier</creatorcontrib><creatorcontrib>Nasser, Mohamed M. S.</creatorcontrib><title>Fast and Accurate Computation of the Logarithmic Capacity of Compact Sets</title><title>Computational methods and function theory</title><addtitle>Comput. Methods Funct. Theory</addtitle><description>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.</description><subject>Analysis</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Conformal mapping</subject><subject>Functions of a Complex Variable</subject><subject>Integral equations</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Numerical analysis</subject><issn>1617-9447</issn><issn>2195-3724</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kLtOwzAUhi0EEqXwAGyWmA0-8Y2MVUQBqRIDMFuuL20qmgTbGfr2OAoDC9MZ_pvOh9At0HugVD0kThkIQkERWlFF4AwtKqgFYari52gBsig15-oSXaV0oFTwmrEFel2blLHpHF5ZO0aTPW764zBmk9u-w33Aee_xpt-Z2Ob9sbW4MYOxbT5N2mQ1NuN3n9M1ugjmK_mb37tEn-unj-aFbN6eX5vVhlgGMhPPQVhlebAuVNJCEEpuZagFN9vAJTBmvHfSPxpbeeZkAOq4la6uhXE2MLZEd3PvEPvv0aesD_0YuzKpy79UCi4KiyWC2WVjn1L0QQ-xPZp40kD1REzPxHQhpidiGkqmmjOpeLudj3-a_w39AFQ4bjs</recordid><startdate>20171201</startdate><enddate>20171201</enddate><creator>Liesen, Jörg</creator><creator>Sète, Olivier</creator><creator>Nasser, Mohamed M. S.</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20171201</creationdate><title>Fast and Accurate Computation of the Logarithmic Capacity of Compact Sets</title><author>Liesen, Jörg ; Sète, Olivier ; Nasser, Mohamed M. S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-e415c7c4fcdf26c1f576b6f954abf46133aeed6e8ac2e3d6f10d4c6d995adcf33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Analysis</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Conformal mapping</topic><topic>Functions of a Complex Variable</topic><topic>Integral equations</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Numerical analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liesen, Jörg</creatorcontrib><creatorcontrib>Sète, Olivier</creatorcontrib><creatorcontrib>Nasser, Mohamed M. S.</creatorcontrib><collection>CrossRef</collection><jtitle>Computational methods and function theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liesen, Jörg</au><au>Sète, Olivier</au><au>Nasser, Mohamed M. S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Fast and Accurate Computation of the Logarithmic Capacity of Compact Sets</atitle><jtitle>Computational methods and function theory</jtitle><stitle>Comput. Methods Funct. Theory</stitle><date>2017-12-01</date><risdate>2017</risdate><volume>17</volume><issue>4</issue><spage>689</spage><epage>713</epage><pages>689-713</pages><issn>1617-9447</issn><eissn>2195-3724</eissn><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.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s40315-017-0207-1</doi><tpages>25</tpages></addata></record> |
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| subjects | Analysis Computational Mathematics and Numerical Analysis Conformal mapping Functions of a Complex Variable Integral equations Mathematics Mathematics and Statistics Numerical analysis |
| title | Fast and Accurate Computation of the Logarithmic Capacity of Compact Sets |
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