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Related papers: Solving Maxwell's Equations with Mimetic Methods

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In this work, we present a comprehensive numerical framework that couples numerical solutions of Maxwell's equations using the Finite-Difference Time-Domain (FDTD) approach, Molecular Dynamics (MD), and the Two-Temperature Model (TTM) to…

Materials Science · Physics 2026-01-29 Othmane Benhayoun , Martin E. Garcia

We consider the numerical discretization of the time-domain Maxwell's equations with an energy-conserving discontinuous Galerkin finite element formulation. This particular formulation allows for higher order approximations of the electric…

Numerical Analysis · Mathematics 2012-01-10 Christoph Koutschan , Christoph Lehrenfeld , Joachim Schoeberl

We present a one-step algorithm that solves the Maxwell equations for systems with spatially varying permittivity and permeability by the Chebyshev method. We demonstrate that this algorithm may be orders of magnitude more efficient than…

Computational Physics · Physics 2009-11-07 H. De Raedt , K. Michielsen , J. S. Kole , M. T. Figge

We consider a system of nonlinear equations that extends the Maxwell theory. It was pointed out in a previous paper that symmetric solutions of these equations display properties characteristic of magnetic oscillations. In this paper I…

Superconductivity · Physics 2007-05-23 Artur Sowa

A more accurate, stable, finite-difference time-domain (FDTD) algorithm is developed for simulating Maxwell's equations with isotropic or anisotropic dielectric materials. This algorithm is in many cases more accurate than previous…

Computational Physics · Physics 2015-06-12 Gregory R. Werner , Carl A. Bauer , John R. Cary

In many time-harmonic electromagnetic wave problems, the considered geometry exhibits an axial symmetry. In this case, by exploiting a Fourier expansion along the azimuthal direction, fully three-dimensional (3D) calculations can be carried…

Numerical Analysis · Mathematics 2022-11-22 Erik Schnaubelt , Nicolas Marsic , Herbert De Gersem

Maxwell's equations are a system of partial differential equations that govern the laws of electromagnetic induction. We study a mimetic finite-difference (MFD) discretization of the equations which preserves important underlying physical…

Numerical Analysis · Mathematics 2021-05-28 James H. Adler , Casey Cavanaugh , Xiaozhe Hu , Ludmil T. Zikatanov

In this paper we propose and analyze finite element discontinuous Galerkin methods for the one- and two-dimensional stochastic Maxwell equations with multiplicative noise. The discrete energy law of the semi-discrete DG methods were…

Numerical Analysis · Mathematics 2022-04-21 Jiawei Sun , Chi-Wang Shu , Yulong Xing

We present a numerical method for solving the free-space Maxwell's equations in three dimensions using compact convolution kernels on a rectangular grid. We first rewrite Maxwell's Equations as a system of wave equations with auxiliary…

Numerical Analysis · Mathematics 2019-07-24 Boris Lo , Phillip Colella

In this paper, we develop two energy-preserving splitting methods for solving three-dimensional stochastic Maxwell equations driven by multiplicative noise. We use operator splitting methods to decouple stochastic Maxwell equations into…

Numerical Analysis · Mathematics 2025-12-30 Liying Zhang , Xinyue Kang , Lihai Ji

A new fast multipole formulation for solving elliptic difference equations on unbounded domains and its parallel implementation are presented. These difference equations can arise directly in the description of physical systems, e.g.…

Computational Physics · Physics 2016-04-08 Sebastian Liska , Tim Colonius

The Maxwell-Bloch equations are a valuable tool to model light-matter interaction, where the application examples range from the description of pulse propagation in two-level media to the elaborate simulation of optoelectronic devices, such…

Quantum Physics · Physics 2021-07-27 Michael Riesch , Christian Jirauschek

In this paper, we develop a structure-preserving discretization of the Lagrangian framework for electromagnetism, combining techniques from variational integrators and discrete differential forms. This leads to a general family of…

Numerical Analysis · Mathematics 2015-11-05 Ari Stern , Yiying Tong , Mathieu Desbrun , Jerrold E. Marsden

A novel unified Hamiltonian approach is proposed to solve Maxwell-Schrodinger equation for modeling the interaction between classical electromagnetic (EM) fields and particles. Based on the Hamiltonian of electromagnetics and quantum…

In this paper we present a methodology for increasing the accuracy and accelerating the convergence of numerical methods for solution of Maxwell's equations in the frequency domain by taking into account the be-havior of the electromagnetic…

Computational Physics · Physics 2021-06-30 Igor Semenikhin

We develop a numerical scheme for solving time-domain Maxwell's equation. The method is motivated by CIP method which uses function values and its derivatives as unknown variables. The proposed scheme is developed by using the Poisson…

Numerical Analysis · Mathematics 2011-10-25 Kazufumi Ito , Tomoya Takeuchi

In this paper we consider the lowest edge-based mimetic finite difference (MFD) discretization in space for Maxwell's equations in cold plasma on rectangular meshes. The method uses a generalized form of mass lumping that, on one hand,…

Numerical Analysis · Mathematics 2016-04-06 V. A. Bokil , V. Gyrya , D. A. McGregor

A new numerical method is presented for solving the rotating shallow water equations on a rotating sphere using quasi-uniform polygonal meshes. The method uses special families of finite element function spaces to mimic key mathematical…

Numerical Analysis · Mathematics 2015-06-23 John Thuburn , Colin J. Cotter

We derive and interpret solutions of time-harmonic Maxwell's equations with a vertical and a horizontal electric dipole near a planar, thin conducting film, e.g. graphene sheet, lying between two unbounded isotropic and non-magnetic media.…

Classical Physics · Physics 2016-05-04 Dionisios Margetis , Mitchell Luskin

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…

Numerical Analysis · Mathematics 2022-02-21 Gang Bao , Mingming Zhang , Xue Jiang , Peijun Li , Xiaokai Yuan