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This article shows how to develop an efficient solver for a stabilized numerical space-time formulation of the advection-dominated diffusion transient equation. At the discrete space-time level, we approximate the solution by using…
We consider the scattering problem on locally perturbed periodic penetrable dielectric layers, which is formulated in terms of the full vector-valued time-harmonic Maxwell's equations. The right-hand side is not assumed to be periodic. At…
Consider the elastic scattering of a time-harmonic wave by multiple well separated rigid particles in two dimensions. To avoid using the complex Green's tensor of the elastic wave equation, we utilize the Helmholtz decomposition to convert…
This paper presents a second-kind surface integral equation method for the numerical solution of frequency-domain electromagnetic scattering problems by locally perturbed layered media in three spatial dimensions. Unlike standard…
The domain integral equation method with its FFT-based matrix-vector products is a viable alternative to local methods in free-space scattering problems. However, it often suffers from the extremely slow convergence of iterative methods,…
We apply the ultraspherical spectral method to solving time-dependent PDEs by proposing two approaches to discretization based on the method of lines and show that these approaches produce approximately same results. We analyze the…
The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be…
We introduce the longitudinal and transverse static surface modes and use them to solve the full-wave electromagnetic scattering problem from penetrable objects. The longitudinal static modes are the eigenmodes with zero surface curl of the…
An exact time-dependent solution for the wave function $\psi(r,t)$ of a particle moving in the presence of an asymmetric rectangular well/barrier potential varying in one dimension is obtained by applying a novel for this problem approach…
Traditional boundary integral methods suffer from the singularity of Green's kernels. The paper develops, for a model problem of 2D scattering as an illustrative example, singularity-free boundary difference equations. Instead of converting…
This work describes and analyzes the domain derivative for a time-dependent acoustic scattering problem. We study the nonlinear operator that maps a sound-soft scattering object to the solution of the time-dependent wave equation evaluated…
A pseudo-spectral method with an absorbing outer boundary is used to solve a set of the time-dependent force-free equations. In the method, both electric and magnetic fields are expanded in terms of the vector spherical harmonic (VSH)…
The scattering of coherent X-rays from dynamically evolving systems is currently becoming experimentally feasible. The scattered beam produces a pattern of bright and dark speckles, which fluctuate almost independently in time and can be…
We report an experimental investigation of the statistical time dynamic of spatial Fourier modes in a fully developped turbulent jet flow. Measurements rely on an original acoustic scattering technique, allowing the direct and continuous…
The multiple scattering of coherent light is a problem of both fundamental and applied importance. In optics, phase conjugation allows spatial focussing and imaging through a multiply scattering medium; however, temporal control is…
A scattering transform defines a locally translation invariant representation which is stable to time-warping deformations. It extends MFCC representations by computing modulation spectrum coefficients of multiple orders, through cascades…
This paper investigates inverse source problems for time-dependent electromagnetic waves governed by Maxwell's equations. After applying the Fourier transform with respect to time, the problem leads to a frequency-domain electromagnetic…
We consider the Green's functions associated to a scalar field propagating on a curved, ultra-static background, in the presence of modified dispersion relations. The usual proper-time deWitt-Schwinger procedure to obtain a series…
The WS time delay matrix relates a lossless and reciprocal system's scattering matrix to its frequency derivative, and enables the synthesis of modes that experience well-defined group delays when interacting with the system. The elements…
We tackle the problem of modeling light scattering in homogeneous translucent material and estimating its scattering parameters. A scattering phase function is one of such parameters which affects the distribution of scattered radiation. It…