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A time domain electric field volume integral equation (TD-EFVIE) solver is proposed for analyzing electromagnetic scattering from dielectric objects with Kerr nonlinearity. The nonlinear constitutive relation that relates electric flux and…
This paper provides a rigorous analysis of boundary element methods for the magnetic field integral equation on Lipschitz polyhedra. The magnetic field integral equation is widely used in practical applications to model electromagnetic…
A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all…
This research thesis presents a novel higher-order spectral element method (SEM) formulated in cylindrical coordinates for analyzing electromagnetic fields in waveguides filled with complex anisotropic media. In this study, we consider a…
We explore how a continuous-variable (CV) quantum computer could solve a classic differential equation, making use of its innate capability to represent real numbers in qumodes. Specifically, we construct variational CV quantum circuits…
The electromagnetic modes and the resonances of homogeneous, finite size, two-dimensional bodies are examined in the frequency domain by a rigorous full wave approach based on an integro-differential formulation of the electromagnetic…
Self consistent solution to electromagnetic (EM)-circuit systems is of significant interest for a number of applications. This has resulted in exhaustive research on means to couple them. In time domain, this typically involves a tight…
We investigate the calculation of resonance modes of a VCSEL with a Riesz projection eigenvalue solver. The eigenvalue solver is based on the principle of contour integration where for the solution of scattering problems physical right…
In this work, the propagation of an ultrasonic pulse in a thin plate is computed solving the differential equations modeling this problem. To solve these equations finite differences are used to discretize the temporal variable, while…
In this paper, we propose a novel high order unfitted finite element method on Cartesian meshes for solving the acoustic wave equation with discontinuous coefficients having complex interface geometry. The unfitted finite element method…
The use of covariant projection finite elements in the efficient 3-D vector finite element analysis of wave guide is presented.
This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document you are assumed to have familiarity with concepts from the…
We develop a spectral low-mode reduced solver for second-order elliptic boundary value problems with spatially varying diffusion coefficients. The approach projects standard finite difference or finite element discretization onto a global…
This paper is concerned with a numerical solution to the scattering of a time-harmonic electromagnetic wave by a bounded and impenetrable obstacle in three dimensions. The electromagnetic wave propagation is modeled by a boundary value…
Finite difference method and finite element method are popular methods for solving groundwater flow equations. This paper presents a new method that uses gradually varied functions to solve such equation. In this paper, we have established…
This paper studies guided transverse scalar modes propagating through helically coiled waveguides. Modeling the modes as solutions of the Helmholtz equation within the three-dimensional (3D) waveguide geometry, a propagation ansatz…
We propose deep-subwavelength optical waveguides based on metal-dielectric multilayer indefinite metamaterials with ultrahigh effective refractive indices. Waveguide modes with different mode orders are systematically analyzed with…
We derive a steady-state, electromagnetic solution for collisional plasma and apply it to computing the total conductance for a vertically stratified ionosphere interrogated by a 3D signal with finite transverse wavelength, which we compare…
This article proposes a novel approach for determining exact solutions to nonlinear ordinary differential equations. The recommended iterative method provides the solution via a rapidly converging series that readily approaches a closed…
We present a semi-analytical approach to compute quasi-guided elastic wave modes in horizontally layered structures radiating into unbounded fluid or solid media. This problem is of relevance, e.g., for the simulation of guided ultrasound…