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We propose a time-domain boundary integral method to model linear wave propagation with refractive, focusing, and Doppler effects arising from medium heterogeneities and moving obstacles. In contrast to existing techniques, our method…
We propose a new approach to model ground penetrating radar signals that propagate through a homogeneous and isotropic medium, and are scattered at thin planar fractures of arbitrary dip, azimuth, thickness and material filling. We use…
Hydrodynamic interactions in a suspension of spherical particles confined between two parallel planar walls are studied under creeping-flow conditions. The many-particle friction matrix in this system is evaluated using our novel numerical…
The paper develops a hybrid method for solving a system of advection--diffusion equations in a bulk domain coupled to advection--diffusion equations on an embedded surface. A monotone nonlinear finite volume method for equations posed in…
We have employed our recently developed Green's function formalism to study the dielectric behavior of a model membrane, formed by two periodic interfaces separating two media of different dielectric constants. The Maxwell's equations are…
A domain integral method employing a specific Green's function (i.e., incorporating some features of the global problem of wave propagation in an inhomogeneous medium) is developed for solving direct and inverse scattering problems relative…
In this paper, we will introduce a new heterogeneous fast multipole method (H-FMM) for 2-D Helmholtz equation in layered media. To illustrate the main algorithm ideas, we focus on the case of two and three layers in this work. The key…
This paper introduces a novel boundary integral equation (BIE) method for the numerical solution of problems of planewave scattering by periodic line arrays of two-dimensional penetrable obstacles. Our approach is built upon a direct BIE…
We have developed a method to simulate multiple electron scattering in a vacuum barrier using real-space single-electron wavefunctions of the separate surfaces. The tunnelling current is calculated to first order in the Dyson series. In…
Surface sensitive electric current measurements are important experimental tools poorly corroborated by theoretical models. We show that the drift-diffusion equations offer a framework for a consistent description of such experiments. The…
We extend density matrix embedding theory to periodic systems, resulting in an electronic band structure method for solid-state materials. The electron correlation can be captured by means of a local impurity model using various choices of…
In this work we developed a new problem solution methodology of contact interaction of acoustic medium with resilient finite bodies of cylindrical form, based on application of boundary integral equations method in conjunction with series…
This paper proposes a frequency-time hybrid solver for the time-dependent wave equation in two-dimensional interior spatial domains. The approach relies on four main elements, namely, 1) A multiple scattering strategy that decomposes a…
We propose an approach for imaging in scattering media when large and diverse data sets are available. It has two steps. Using a dictionary learning algorithm the first step estimates the true Green's function vectors as columns in an…
In biomimetic and biological systems, interactions between surfaces are often mediated by adhesive molecules, nanoparticles, or colloids dispersed in the surrounding solution. We present here a general, statistical-mechanical model for two…
This paper proposes an isogeometric boundary element method (IGBEM) to solve the electromagnetic scattering problems for three-dimensional doubly-periodic multi-layered structures. The main concerns are the constructions of (i) an open…
We present a barrier method for treating frictional contact on interfaces embedded in finite elements. The barrier treatment has several attractive features, including: (i) it does not introduce any additional degrees of freedom or…
An accurate method for designing transmissive metasurfaces is presented that provides perfect transmission while transforming the amplitude and phase of the wavefront. The designed metasurfaces consist of three spatially-varying, electric…
We study interaction induced topological phase transition in Bernevig-Hughes-Zhang model. Topological nature of the phase transition is revealed by directly calculating the Z2 index of the interacting system from the single-particle Green's…
A surface integral representation of Maxwell's equations allows the efficient electromagnetic (EM) modeling of three-dimensional structures with a two-dimensional discretization, via the boundary element method (BEM). However, existing BEM…