Adaptive Wavelet Methods on Unbounded Domains

In this paper, we introduce an adaptive wavelet method for operator equations on unbounded domains. We use wavelet bases on ℝ n to equivalently express the operator equation in terms of a well-conditioned discrete problem on sequence spaces. By realizing an approximate adaptive operator application...

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Bibliographic Details
Published inJournal of scientific computing Vol. 53; no. 2; pp. 342 - 376
Main Authors Kestler, Sebastian, Urban, Karsten
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.11.2012
Springer Nature B.V
Subjects
Algorithms
Computational Mathematics and Numerical Analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
Wavelet analysis
Unbounded domains
Wavelets
Adaptive numerical methods
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Summary:In this paper, we introduce an adaptive wavelet method for operator equations on unbounded domains. We use wavelet bases on ℝ n to equivalently express the operator equation in terms of a well-conditioned discrete problem on sequence spaces. By realizing an approximate adaptive operator application also for unbounded domains, we obtain a scheme that is convergent at an asymptotically optimal rate. We show the quantitative performance of the scheme by various numerical experiments.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-011-9573-4