Conditioning analysis for discrete Helmholtz problems
- In this paper, we examine conditioning of the discretization of the Helmholtz problem. Although the discrete Helmholtz problem has been studied from different perspectives, to the best of our knowledge, there is no conditioning analysis for it. We aim to fill this gap in the literature. We propose a novel method in 1D to observe the near-zero eigenvalues of a symmetric indefinite matrix. Standard classification of ill-conditioning based on the matrix condition number is not true for the discrete Helmholtz problem. We relate the ill-conditioning of the discretization of the Helmholtz problem with the condition number of the matrix. We carry out analytical conditioning analysis in 1D and extend our observations to 2D with numerical observations. We examine several discretizations. We find different regions in which the condition number of the problem shows different characteristics. We also explain the general behavior of the solutions in these regions.
Verfasserangaben: | Adem KayaORCiD, Melina A. FreitagORCiDGND |
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DOI: | https://doi.org/10.1016/j.camwa.2022.05.016 |
ISSN: | 0898-1221 |
ISSN: | 1873-7668 |
Titel des übergeordneten Werks (Englisch): | Computers and mathematics with applications : an international journal |
Verlag: | Elsevier Science |
Verlagsort: | Amsterdam |
Publikationstyp: | Wissenschaftlicher Artikel |
Sprache: | Englisch |
Datum der Erstveröffentlichung: | 15.07.2022 |
Erscheinungsjahr: | 2022 |
Datum der Freischaltung: | 07.02.2023 |
Freies Schlagwort / Tag: | Condition number; Helmholtz problem; Ill-conditioning; Indefinite; matrices |
Band: | 118 |
Seitenanzahl: | 12 |
Erste Seite: | 171 |
Letzte Seite: | 182 |
Organisationseinheiten: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC-Klassifikation: | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik |
5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik | |
Peer Review: | Referiert |