Related papers: A Bloch wave numerical scheme for scattering probl…
Consider the time-domain multiple cavity scattering problem, which arises in diverse scientific areas and has significant industrial and military applications. The multiple cavity embedded in an infinite ground plane, is filled with…
We present a systematic numerical approach to compute the eigenmodes and the related eigenfrequencies of a disordered photonic crystal, characterized by small fluctuations of the otherwise periodic dielectric profile. The field eigenmodes…
This paper concerns an inverse elastic scattering problem which is to determine a rigid obstacle from time domain scattered field data for a single incident plane wave. By using Helmholtz decomposition, we reduce the initial-boundary value…
Passive imaging involves recording waves generated by uncontrolled, random sources and utilizing correlations of such waves to image the medium through which they propagate. In this paper, we focus on passive inverse obstacle scattering…
The subject of this paper is multigrid solvers for Helmholtz operators with large wave numbers. Algorithms presented here are variations of the wave-ray solver which is modified to allow efficient solutions for operators with constant,…
We propose a novel on-surface radiation condition to approximate the outgoing solution to the Helmholtz equation in the exterior of several impenetrable convex obstacles. Based on a local approximation of the Dirichlet-to-Neumann operator…
Diffraction tomography is a noninvasive technique that estimates the refractive indices of unknown objects and involves an inverse-scattering problem governed by the wave equation. Recent works have shown the benefit of nonlinear models of…
The Helmholtz equation is notoriously difficult to solve with standard numerical methods, increasingly so, in fact, at higher frequencies. Controllability methods instead transform the problem back to the time-domain, where they seek the…
Consider the one-dimensional stochastic Helmholtz equation where the source is assumed to be driven by the white noise. This paper concerns the stability analysis of the inverse random source problem which is to reconstruct the statistical…
This paper introduces a novel boundary integral approach of shape uncertainty quantification for the Helmholtz scattering problem in the framework of the so-called parametric method. The key idea is to construct an integration grid whose…
Scattering of a time harmonic anti-plane shear wave due to either a pair of crack tips or a pair of rigid constraint tips on square lattice is considered. The two problems correspond to the so called zero-offset case of scattering due to a…
We study wave scattering by a finite transversal strip in a discrete square-lattice waveguide with Dirichlet boundary conditions imposed on the strip and the waveguide walls. The setting is motivated as a discrete analogue of the classical…
This paper investigates the inverse scattering problem of time-harmonic plane waves incident on a perfectly reflecting random periodic structure. To simulate random perturbations arising from manufacturing defects and surface wear in…
We use the work of Milton, Seppecher, and Bouchitt\'{e} on variational principles for waves in lossy media to formulate a finite element method for solving the complex Helmholtz equation that is based entirely on minimization. In…
In this paper, we develop an accurate and efficient framework for computing subwavelength guided modes in high-contrast periodic media with line defects, based on a tight-binding approximation. The physical problem is formulated as an…
This paper focuses on the well-posedness (or lack thereof) of three-dimensional time-harmonic wave propagation problems modeled by the Helmholtz equation. It is well-known that if the problem is set in bounded domain with Dirichlet boundary…
A numerical technique is described that can efficiently compute solutions in interface problems. These are problems with data, such as the coefficients of differential equations, discontinuous or even singular across one or more interfaces.…
Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…
Asymptotic solution to many-body wave scattering problem is given in the case of many small scatterers. The small scatterers can be particles whose physical properties are described by the boundary impedances, or they can be small…
Numerically solving the 2D Helmholtz equation is widely known to be very difficult largely due to its highly oscillatory solution, which brings about the pollution effect. A very fine mesh size is necessary to deal with a large wavenumber…