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The height of dielectric metasurfaces is largely considered a constant in the fabrication process due to the top-down fabrication approach, resulting in a binary structure. Yet, for the recently introduced Mie voids metasurfaces,…
The non-linear coupled Gross-Pitaevskii equation governing the dynamics of the two component Bose-Einstein condensate (TBEC) is shown to admit pure sinusoidal, propagating wave solutions in quasi one dimensional geometry. These solutions,…
Implementing computational boundary conditions, such as perfectly matched layers PML does have advantages for forwarding modeling of the earth's crust. The mathematical modeling of many physical problems encountered in industrial…
We introduce a rigorous and simple method for analyzing metasurfaces, modeled as zero-thickness electromagnetic sheets, in Finite Difference (FD) techniques. The method consists in describing the spatial discontinuity induced by the…
This paper devotes to developing novel boundary integral equation (BIE) solvers for the problem of thermoelastic scattering by open-arcs with four different boundary conditions in two dimensions. The proposed methodology is inspired by the…
For backward stochastic Volterra integral equations (BSVIEs, for short), under some mild conditions, the so-called adapted solutions or adapted M-solutions uniquely exist. However, satisfactory regularity of the solutions is difficult to…
A new parallel solver for the volumetric integral equations (IE) of electrodynamics is presented. The solver is based on the Galerkin method which ensures the convergent numerical solution. The main features include: (i) the memory usage is…
The numerical simulation of rarefied gas mixtures with disparate mass and concentration is a huge research challenge. Based on our recent kinetic modelling for monatomic gas mixture flows, this problem is tackled by the general synthetic…
We investigate the possibility to model a metasurface, defined as a zero-thickness sheet of surface polarization currents, by a thin slab, characterized by a subwavelength thickness and usual voluminal medium parameters. First, we elaborate…
While metasurfaces (MSs) are constructed from deeply-subwavelength unit cells, they are generally electrically large and full-wave simulations of the complete structure are computationally expensive. Thus, to reduce this high computational…
We present a new class of well conditioned integral equations for the solution of two and three dimensional scattering problems by homogeneous penetrable scatterers. Our novel boundary integral equations result from suitable representations…
In this paper, the notion of singular backward stochastic Volterra integral equations (singular BSVIEs for short) in infinite dimensional space is introduced, and the corresponding well-posedness is carefully established. A class of…
A preconditioned, multipole-accelerated, Krylov-subspace iterative algorithm for the electromagnetic scattering analysis of three dimensional (3D), arbitrary shaped dielectric structures composed of single and multi-layered dielectric…
Generalized Chebyshev iteration (GCI) applied for solving linear equations with nonselfadjoint operators is considered. Sufficient conditions providing the convergence of iterations imposed on the domain of localization of the spectrum on…
Using a dipole interaction model, we derive generalized sheet transition conditions (GSTCs) for electromagnetic fields at the surface of a metascreen consisting of an array of arbitrarily shaped apertures in a perfectly conducting screen of…
Heat-flux boundary conditions are challenging to implement efficiently in rarefied gas flow simulations because the wall-reflected gas temperature and density must be determined dynamically during the computation. This paper aims to tackle…
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…
This work primarily focuses on the study of three gradient reconstruction techniques applied to the calculation of viscous terms in a cell-centered, finite volume formulation for general unstructured grids. The work also addresses different…
We show that a properly designed bianisotropic metasurface placed at the interface between two arbitrary different media, or coating a dielectric medium exposed to the air, provides Brewster (reflectionless) transmission at arbitrary angles…
We present in this work a new reconstruction scheme, so-called MUSCL-THINC-BVD scheme, to solve the five-equation model for interfacial two phase flows. This scheme employs the traditional shock capturing MUSCL (Monotone Upstream-centered…