Convergence analysis with parameter estimates for a reduced basis acoustic scattering T-matrix method

M. Ganesh*, S. C. Hawkins, R. Hiptmair

*Corresponding author for this work

    Research output: Contribution to journalArticle

    15 Citations (Scopus)

    Abstract

    The celebrated truncated T-matrix method for wave propagation models belongs to a class of the reduced basis methods (RBMs), with the parameters being incident waves and incident directions. The T-matrix characterizes the scattering properties of the obstacles independent of the incident and receiver directions. In the T-matrix method the reduced set of basis functions for representation of the scattered field is constructed analytically and hence, unlike other classes of the RBM, the T-matrix RBM avoids computationally intensive empirical construction of a reduced set of parameters and the associated basis set. However, establishing a convergence analysis and providing practical a priori estimates for reducing the number of basis functions in the T-matrix method has remained an open problem for several decades. In this work we solve this open problem for time-harmonic acoustic scattering in two and three dimensions. We numerically demonstrate the convergence analysis and the a priori parameter estimates for both point-source and plane-wave incident waves. Our approach can be used in conjunction with any numerical method for solving the forward wave propagation problem.

    Original languageEnglish
    Pages (from-to)1348-1374
    Number of pages27
    JournalIMA Journal of Numerical Analysis
    Volume32
    Issue number4
    DOIs
    Publication statusPublished - Oct 2012

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