Fulltext

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

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

In: Ima Journal of Numerical Analysis, 2012, vol. 32, no. 4, p. 1348-1374

Add to personal list
    Title
    • Convergence analysis with parameter estimates for a reduced basis acoustic scattering T-matrix method
    Author
    • Ganesh, M.. Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO 80401, USA
    • Hawkins, S. C.. Department of Mathematics, Macquarie University, Sydney, NSW 2109, Australia, stuart.hawkins@mq.edu.au
    • Hiptmair, R.. Seminar für Angewandte Mathematik, ETH Zurich, CH-8092 Zürich, Switzerland, hiptmair@sam.math.ethz.ch
    Document Type
    • Postprint
    Language
    • English
    Published in
    • Ima Journal of Numerical Analysis, 2012, vol. 32, no. 4, p. 1348-1374. Oxford University Press
    Other Version
    OAI-PMH Identifier
    • oai:doc.rero.ch:302263
    Summary
    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