Imaging and Computing Seminar
David Nicholls, Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago
A Boundary Perturbation Method for Interface Reconstruction via Constrained Quadratic Optimization
Grating scattering is a fundamental model in acoustics, electromagnetics, nanoscience, and the geosciences. In this talk 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 the success of 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 numerous numerical experiments 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.