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

by M. Ganesh and S. Hawkins and R. Hiptmair

(Report number 2011-04)

Abstract
The reduced basis method is an offline/online process for the approximation of functional outputs of parameterized mathematical models. The offline process is for solutions of the models for a reduced finite set of parameters and the online process provides the option of quickly obtaining the functional outputs for an infinite choice of parameters in the model. For reliability of the offline/online process, it is important to establish convergence analysis of the reduced basis method and provide a practical estimate for optimal reduction of parameters. The choice of reduced parameters is usually obtained using some optimization technique. For wave propagation models, with the parameters being incident waves and directions, the celebrated T-matrix method is an optimization-free reduced basis method. However, establishing convergence analysis and providing practical estimates of truncation parameters for 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, with an optimization-free reduced basis T-matrix method. We numerically demonstrate the convergence analysis and 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.

Keywords: Wave propagation, Acoustic Scattering, T-matrix

@Techreport{GHH11_63,
  author = {M. Ganesh and S. Hawkins and R. Hiptmair},
  title = {Convergence analysis with parameter estimates for a reduced basis acoustic scattering t-matrix method},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2011-04},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2011/2011-04.pdf },
  year = {2011}
}

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