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Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an…
We present a mimetic finite-difference approach for solving Maxwell's equations in one and two spatial dimensions. After introducing the governing equations and the classical Finite-Difference Time-Domain (FDTD) method, we describe mimetic…
We present a higher-order finite volume method for solving elliptic PDEs with jump conditions on interfaces embedded in a 2D Cartesian grid. Second, fourth, and sixth order accuracy is demonstrated on a variety of tests including problems…
We propose a finite-difference algorithm for solving the time-dependent Ginzburg-Landau (TDGL) equation coupled to the appropriate Maxwell equation. The time derivatives are discretized using a second order semi-implicit scheme which, for…
An efficient finite-difference time-domain (FDTD) algorithm is built to solve the transverse electric 2D Maxwell's equations with inhomogeneous dielectric media where the electric fields are discontinuous across the dielectric interface.…
In this paper we present a multigrid approach to solve the Poisson equation in arbitrary domain (identified by a level set function) and mixed boundary conditions. The discretization is based on finite difference scheme and ghost-cell…
Simulation of 3D low-frequency electromagnetic fields propagating in the Earth is computationally expensive. We present a fictitious wave domain high-order finite-difference time-domain (FDTD) modelling method on nonuniform grids to compute…
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…
We present a finite-element time-domain (FETD) Maxwell solver for the analysis of body-of-revolution (BOR) geometries based on discrete exterior calculus (DEC) of differential forms and transformation optics (TO) concepts. We explore TO…
We develop a high order accurate numerical method for solving the elastic wave equation in second-order form. We hybridize the computationally efficient Cartesian grid formulation of finite differences with geometrically flexible…
This paper introduces new discretization schemes for time-harmonic Maxwell equations in a connected domain by using the weak Galerkin (WG) finite element method. The corresponding WG algorithms are analyzed for their stability and…
The aim of this article is to present a hybrid finite element/finite difference method which is used for reconstructions of electromagnetic properties within a realistic breast phantom. This is done by studying the mentioned properties'…
A hybrid Maxwell solver for fully relativistic and electromagnetic (EM) particle-in-cell (PIC) codes is described. In this solver, the EM fields are solved in $k$ space by performing an FFT in one direction, while using finite difference…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
Consider the diffraction of an electromagnetic plane wave by a biperiodic structure where the wave propagation is governed by the three-dimensional Maxwell equations. Based on transparent boundary condition, the grating problem is…
We present a transmission line theory of exceptional points of degeneracy (EPD) in coupled-mode guiding structures, i.e., a theory that illustrates the characteristics of coupled electromagnetic modes under a special dispersion degeneracy…
A crucial part of successful wave propagation related inverse problems is an efficient and accurate numerical scheme for solving the seismic wave equations. In particular, the numerical solution to a multi-dimensional Helmholtz equation can…
New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…
The locally modified finite element method, which is introduced in [Frei, Richter: SINUM 52(2014), p. 2315-2334], is a simple fitted finite element method that is able to resolve weak discontinuities in interface problems. The method is…
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…