Abstract
Consider a time-harmonic acoustic wave incident onto a doubly periodic (biperiodic) interface from a homogeneous compressible inviscid fluid. The region below the interface is supposed to be an isotropic linearly elastic solid. This paper is concerned with the inverse fluid-solid interaction (FSI) problem of recovering the unbounded periodic interface separating the fluid and solid. We provide a theoretical justification of the factorization method for precisely characterizing the region occupied by the elastic solid by utilizing the scattered acoustic waves measured in the fluid. A computational criterion and a uniqueness result are presented with infinitely many incident acoustic waves having common quasiperiodicity parameters. Numerical examples in 2D are demonstrated to show the validity and accuracy of the inversion algorithm.
Highlights
IntroductionConsider a time-harmonic acoustic wave incident onto an unbounded doubly periodic (or bi-periodic) surface from above
Consider a time-harmonic acoustic wave incident onto an unbounded doubly periodic surface from above
The medium above the surface is supposed to be filled with homogeneous compressible inviscid fluid with a constant mass density, whereas the region below is occupied by an isotropic linearly elastic solid characterized by the Lame constants
Summary
Consider a time-harmonic acoustic wave incident onto an unbounded doubly periodic (or bi-periodic) surface from above. Our paper concerns the inverse FSI problem of recovering the unbounded periodic interface separating the fluid and solid from knowledge of the scattered acoustic waves measured in the fluid. Inspired by earlier factorization methods for diffraction gratings [1] and for bounded obstacles in a half-space [24, Chapter 2.6], we utilize a set of incident acoustic waves with common quasiperiodicity parameters to factorize the near-field operator arising from our inverse FSI problem.
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