Paolo Amore , John P. Boyd , Natalia Tene Sandoval
{"title":"Isospectral heterogeneous domains: A numerical study","authors":"Paolo Amore , John P. Boyd , Natalia Tene Sandoval","doi":"10.1016/j.jcpx.2019.100018","DOIUrl":null,"url":null,"abstract":"<div><p>We have applied the finite differences method to the study of a pair of isospectral heterogeneous domains, first introduced in Ref. <span>[1]</span>. We show that Richardson and Padé-Richardson extrapolations can be used (as in the homogeneous case) to obtain very precise approximations to the lowest eigenvalues. We have found that the first few exponents of the asymptotic series for the finite difference eigenvalues are unchanged with from the homogeneous case. Additionally, we have improved the previous best estimates for the case of homogeneous isospectral domains, obtaining 10 extra correct digits for the fundamental mode (and similar results for the other eigenvalues), with respect to the best result previously available.</p></div>","PeriodicalId":37045,"journal":{"name":"Journal of Computational Physics: X","volume":"1 ","pages":"Article 100018"},"PeriodicalIF":0.0000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jcpx.2019.100018","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Physics: X","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2590055219300344","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
We have applied the finite differences method to the study of a pair of isospectral heterogeneous domains, first introduced in Ref. [1]. We show that Richardson and Padé-Richardson extrapolations can be used (as in the homogeneous case) to obtain very precise approximations to the lowest eigenvalues. We have found that the first few exponents of the asymptotic series for the finite difference eigenvalues are unchanged with from the homogeneous case. Additionally, we have improved the previous best estimates for the case of homogeneous isospectral domains, obtaining 10 extra correct digits for the fundamental mode (and similar results for the other eigenvalues), with respect to the best result previously available.
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