Related papers: Computation of Maxwell's equations on Manifold usi…
Complementing a study which was published in this journal in 2005, we present explicit calculations of fields predicted by Maxwell's equations both in Lorenz and in Coulomb gauge. Analytic expressions are obtainable, when the source of the…
We present a stability and convergence analysis of the space-time continuous finite element method for the Hamiltonian formulation of the wave equation. More precisely, we prove a continuous dependence of the discrete solution on the data…
The complex form of Maxwell equations has been constructed as one equation for 3-dimensional complex A-vector. The real and imaginary parts of this vector are described with use of electric and magnetic tensions accordingly. With using a…
The article is devoted to application of tensorial formalism for derivation of different types of Maxwell's equations. The Maxwell's equations are written in the covariant coordinate-free and the covariant coordinate forms. Also the…
This note offers a conceptually straightforward and efficient way to formulate and solve problems in the electromagnetics of moving media based on a representation of Maxwell's equations in terms of differential forms on spacetime together…
Numerical discretization of the large-scale Maxwell's equations leads to an ill-conditioned linear system that is challenging to solve. The key requirement for successive solutions of this linear system is to choose an efficient solver. In…
The propagation of electromagnetic waves in general media is modeled by the time-dependent Maxwell's partial differential equations (PDEs), coupled with constitutive laws that describe the response of the media. In this work, we focus on…
The features of propagation of intense waves are of great interest for theory and experiment in electrodynamics and acoustics. The behavior of nonlinear waves in a bounded volume is of especial importance and, at the same time, is an…
We propose an arbitrarily higher (even) order implicit leapfrog scheme for time discretization of a three-field formulation of Maxwell's equations. We use this in conjunction with an arbitrarily higher-order and compatible discretization…
The first order by time partial differential equations are used as models in applications such as fluid flow, heat transfer, solid deformation, electromagnetic waves, and others. In this paper we propose the new numerical method to solve a…
The application of Regge calculus, a lattice formulation of general relativity, is reviewed in the context of numerical relativity. Particular emphasis is placed on problems of current computational interest, and the strengths and…
In this and a set of companion whitepapers, the USQCD Collaboration lays out a program of science and computing for lattice gauge theory. These whitepapers describe how calculation using lattice QCD (and other gauge theories) can aid the…
In this work, we develop a space--time Chebyshev spectral collocation method for three-dimensional Maxwell's equations and combine it with tensor-network techniques in Tensor-Train (TT) format. Under constant material parameters, the…
Performing analog computations with metastructures is an emerging wave-based paradigm for solving mathematical problems. For such devices, one major challenge is their reconfigurability, especially without the need for a priori mathematical…
The time domain enclosure method is one of analytical methods for inverse obstacle problems governed by partial differential equations in the time domain. This paper considers the case when the governing equation is given by the Maxwell…
We compute the waves propagating on a compact 3-manifold of constant positive curvature with a non trivial topology: the Poincar\'e dodecahedral space that is a plausible model of multi-connected universe. We transform the Cauchy problem to…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
This is the second in a series of papers in which we take a systematic study of gauge field theories such as the Maxwell equations and the Yang-Mills equations, on curved space-times. In this paper, we study the Maxwell equations in the…
We explore the mathematical consequences of the assumption of a discrete space-time. The fundamental laws of physics have to be translated into the language of discrete mathematics. We find integral transformations that leave the lattice of…
We study a system of Maxwell's equations that describes the time evolution of electromagnetic fields with an additional electric scalar variable to make the system amenable to a mixed finite element spatial discretization. We demonstrate…