| dc.contributor.author | Liesen, Jörg | |
| dc.contributor.author | Nasser, Mohamed M. S. | |
| dc.contributor.author | Sète, Olivier | |
| dc.date.accessioned | 2023-03-06T20:43:16Z | |
| dc.date.available | 2023-03-06T20:43:16Z | |
| dc.date.issued | 2023-02-28 | |
| dc.identifier.citation | Liesen, J., Nasser, M.M.S. & Sète, O. Computing the logarithmic capacity of compact sets having (infinitely) many components with the charge simulation method. Numer Algor (2023). https://doi.org/10.1007/s11075-022-01428-2 | |
| dc.identifier.issn | 1572-9265 | |
| dc.identifier.uri | https://doi.org/10.1007/s11075-022-01428-2 | |
| dc.identifier.uri | https://soar.wichita.edu/handle/10057/25058 | |
| dc.description | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. | |
| dc.description.abstract | We apply the charge simulation method (CSM) in order to compute the logarithmic capacity of compact sets consisting of (infinitely) many “small” components. This application allows to use just a single charge point for each component. The resulting method therefore is significantly more efficient than methods based on discretizations of the boundaries (for example, our own method presented in Liesen et al. (Comput. Methods Funct. Theory 17, 689–713, 2017)), while maintaining a very high level of accuracy. We study properties of the linear algebraic systems that arise in the CSM, and show how these systems can be solved efficiently using preconditioned iterative methods, where the matrix-vector products are computed using the fast multipole method. We illustrate the use of the method on generalized Cantor sets and the Cantor dust. | |
| dc.language.iso | en_US | |
| dc.publisher | Springer Link | |
| dc.relation.ispartofseries | Numerical Algorithms | |
| dc.relation.ispartofseries | 2023 | |
| dc.subject | Logarithmic capacity | |
| dc.subject | Charge simulation method | |
| dc.subject | Cantor set | |
| dc.subject | Cantor dust | |
| dc.subject | Fast multipole method | |
| dc.subject | GMRES method | |
| dc.title | Computing the logarithmic capacity of compact sets having (infinitely) many components with the charge simulation method | |
| dc.type | Article | |
| dc.rights.holder | © 2023, The Author(s) | |
