Open Access

ARTICLE

Continuation Schemes for Shape Detection in Inverse Acoustic Scattering Problems

by S.-W. Na¹, L.F. Kallivokas²

1 Department of Civil, Architectural and Environmental Engineering, The University of Texas at Austin, Austin, TX, USA.
2 Department of Civil, Architectural and Environmental Engineering, The University of Texas at Austin, Austin, TX, USA.

Computer Modeling in Engineering & Sciences 2008, 35(1), 73-90. https://doi.org/10.3970/cmes.2008.035.073

Abstract

We discuss simple numerical schemes, termed continuation schemes, for detecting the location and shape of a scatterer embedded in a host acoustic medium, when considering scant measurements of the scattered acoustic pressure in the vicinity (near- or far-field) of the obstacle. The detection is based on incomplete information, i.e., the measurement stations are distributed in the backscatter region and do not circumscribe the sought scatterer. We consider sound-hard scatterers, and use boundary integral equations for the underlying numerical scheme. We favor amplitude-based misfit functionals, and use frequency- and directionality-continuation schemes to resolve the scatterer's location and shape. We report on numerical experiments that attest to the promise of the schemes.

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