Operator expansions and constrained quadratic optimization for interface reconstruction: Impenetrable periodic acoustic media

Malcolm, Alison and Nicholls, David (2014) Operator expansions and constrained quadratic optimization for interface reconstruction: Impenetrable periodic acoustic media. Wave Motion, 51 (1). pp. 23-40. ISSN 0165-2125

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Abstract

Grating scattering is a fundamental model in remote sensing, electromagnetics, ocean acoustics, nondestructive testing, and image reconstruction. In this work, we examine the problem of detecting the geometric properties of gratings in a two-dimensional acoustic medium where the fields are governed by the Helmholtz equation. Building upon our previous Boundary Perturbation approach (implemented with the Operator Expansions formalism) we derive a new approach which augments this with a new “smoothing” mechanism. With numerical simulations we demonstrate the enhanced stability and accuracy of our new approach which further suggests not only a rigorous proof of convergence, but also a path to generalizing the algorithm to multiple layers, three dimensions, and the full equations of linear elasticity and Maxwell’s equations.

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