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Adaptive Wavelet Methods on Unbounded Domains

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Abstract

In this paper, we introduce an adaptive wavelet method for operator equations on unbounded domains. We use wavelet bases on ℝn 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.

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Authors and Affiliations

  1. Institute for Numerical Mathematics, University of Ulm, Helmholtzstrasse 18, 89069, Ulm, Germany

    Sebastian Kestler & Karsten Urban

Authors
  1. Sebastian Kestler
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  2. Karsten Urban
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Correspondence to Karsten Urban.

Additional information

This work has been supported by the Deutsche Forschungsgemeinschaft within the Research Training Group (Graduiertenkolleg) GrK1100 Modellierung, Analyse und Simulation in der Wirtschaftsmathematik at the University of Ulm and within the priority program DFG-SPP 1324 Mathematical methods for extracting quantifiable information from complex systems.

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Kestler, S., Urban, K. Adaptive Wavelet Methods on Unbounded Domains. J Sci Comput 53, 342–376 (2012). https://doi.org/10.1007/s10915-011-9573-4

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  • DOI: https://doi.org/10.1007/s10915-011-9573-4

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