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COMPUTATIONAL METHODS FOR ACOUSTICS PROBLEMS
Edited by: F. Magoulès
Inverse Acoustic Problems
Department of Mathematics, California State University, Northbridge CA, United States of America
R. Djellouli, "Inverse Acoustic Problems", in F. Magoulès, (Editor), "Computational Methods for Acoustics Problems", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 10, pp 263-294, 2008. doi:10.4203/csets.18.10
Keywords: acoustic scattering, inverse obstacle problem, ill-posed problem, Newton method, Tikhonov regularization, Fréchet derivative, sensitivity analysis, finite element method, domain decomposition method.
We report on the performance of a regularized Newton solution methodology for retrieving the shape of an impenetrable three-dimensional obstacle from the intensity measurements of its corresponding acoustic far-field pattern. The main features of this optimization procedure are: (a) a sensitivity-based and frequency-aware multi-stage solution strategy, (b) a computationally efficient usage of the exact sensitivities of the far-field pattern to the specified shape parameters, and (c) a numerically scalable domain decomposition method for the fast solution in a frequency band of three-dimensional direct acoustic scattering problems. Numerical results obtained in the case of three-dimensional inverse mockup submarine problems are presented to illustrate the salient features of this computational methodology and highlight its performance characteristics.
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