Related papers: Spurious-mode-free finite element method for scatt…
In this paper we develop a numerical method for solving an inverse scattering problem of estimating the scattering potential in a Schr\"{o}dinger equation from frequency domain measurements based on reduced order models (ROM). The ROM is a…
The effects of thermal diffuse scattering on the transmission and eventual diffraction of highly accelerated electrons are investigated with a method that incorporates the frozen phonon approximation to the exact numerical solution of the…
Reflection of particles from a disordered or chaotic medium is characterized by a scattering matrix that can be represented as a superposition of resonances. Each resonance corresponds to an eigenstate inside the medium and has a width…
In spite of their importance for understanding phonon transport phenomena in thin films and polycrystalline solids, the effects of boundary roughness scattering on phonon specularity and coherence are poorly understood because there is no…
We consider radial complex scaling/perfectly matched layer methods for scalar resonance problems in homogeneous exterior domains. We introduce a new abstract framework to analyze the convergence of domain truncations and discretizations.…
We consider in this work an inverse acoustic scattering problem when only phaseless data is available. The inverse problem is highly nonlinear and ill-posed due to the lack of the phase information. Solving inverse scattering problems with…
We consider an inner problem for whispering gallery high-frequency asymptotic mode's scattering by a boundary inflection. The related boundary-value problem for a Schr\"{o}dinger equation on a half-line with a potential linear in both space…
We present several applications of mode matching methods in spectral and scattering problems. First, we consider the eigenvalue problem for the Dirichlet Laplacian in a finite cylindrical domain that is split into two subdomains by a…
In this paper we develop a numerical scheme based on quadratures to approximate solutions of integro-differential equations involving convolution kernels, $\nu$, of diffusive type. In particular, we assume $\nu$ is symmetric and…
Diffusion models are powerful tools for sampling from high-dimensional distributions by progressively transforming pure noise into structured data through a denoising process. When equipped with a guidance mechanism, these models can also…
In this thesis we address a series of new problems in non-hermitian optical scattering with increasing degrees of complexity. We develop the theory of reflectionless scattering modes, introducing a novel and broad class of impedance-matched…
We present the most complete scattering theory for noise in noninteracting case. The exact formula for spectral density of current fluctuations at finite frequency is presented in terms of scattering matrix for a coherent quantum conductor.…
Discrete ordinate ($S_N$) and filtered spherical harmonics ($FP_N$) based schemes have been proven to be robust and accurate in solving the Boltzmann transport equation but they have their own strengths and weaknesses in different physical…
In this work, our aim is to reconstruct the unknown initial value from terminal data. We develop a numerical framework on nonuniform time grids for fractional wave equations under the lower regularity assumptions. Then, we introduce a…
The goal of the present work is to solve a linear dispersive equation with variable coefficient advection on an unbounded domain. In this setting, transparent boundary conditions are vital to allow waves to leave (or even re-enter) the,…
This paper concerns the inverse source scattering problems of recovering random sources for acoustic and elastic waves. The underlying sources are assumed to be random functions driven by an additive white noise. The inversion process aims…
In this paper we propose and analyze a fully discrete method for a direct boundary integral formulation of the scattering of a transient acoustic wave by a sound-soft obstacle. The method uses Galerkin-BEM in the space variables and three…
We consider frequency-domain acoustic scattering at a homogeneous star-shaped penetrable obstacle, whose shape is uncertain and modelled via a radial spectral parameterization with random coefficients. Using recent results on the stability…
The propagation of the transverse electric (TE) and transverse magnetic (TM) waves in an effectively two-dimensional (2D) isotropic medium is described by Bergmann's equation of acoustics. We develop a dynamical formulation of the…
We introduce a \textit{non-modal} analysis technique that characterizes the diffusion properties of spectral element methods for linear convection-diffusion systems. While strictly speaking only valid for linear problems, the analysis is…