scholarly journals Degenerate forms of Maxwell's equations

1990 ◽  
Vol 31 (3) ◽  
pp. 277-300
Author(s):  
A. L. Carey ◽  
K. McNamara
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell Equations ◽  
Maxwell's Equations ◽  
Regularity Of Solutions ◽  
Degenerate Equations ◽  
Degenerate Elliptic ◽  
Modelling Problems

AbstractThis paper studies degenerate forms of Maxwell's equations which arise from approximations suggested by geophysical modelling problems. The approximations reduce Maxwell's equations to degenerate elliptic/parabolic ones. Here we consider the questions of existence, uniqueness and regularity of solutions for these equations and address the problem of showing that the solutions of the degenerate equations do approximate those of the genuine Maxwell equations.

scholarly journals Calderón problem for Maxwell's equations in two dimensions

2016 ◽  
Vol 24 (3) ◽  
Author(s):  
Oleg Y. Imanuvilov ◽  
Masahiro Yamamoto
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell Equations ◽  
Maxwell's Equations ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Global Uniqueness ◽  
Calderón Problem ◽  
Dirichlet To Neumann Map

AbstractWe prove the global uniqueness in determination of the conductivity, the permeability and the permittivity of the two-dimensional Maxwell equations by the partial Dirichlet-to-Neumann map limited to an arbitrary subboundary.

scholarly journals Calculation of Maxwell’s Equations Using MATLAB

2021 ◽  
Vol 09 (10) ◽  
Author(s):  
Subhi Abdalazim Aljily Osman ◽  
Keyword(s):  
Mathematical Method ◽  
Analytical Solution ◽  
Maxwell’S Equations ◽  
Maxwell Equations ◽  
Maxwell's Equations ◽  
System Of Equations ◽  
First Order ◽  
Mathematical Programs ◽  
Mathematical Problems ◽  
Micro Radio

Maxwell’s equations describe electromagnetic Phenomena. This includes micro- , radio and radar waves .The Maxwell equations are discussed in more detail Faraday's and Amperes laws constitute a first - order hyperbolic system of equations .Matlab is one of the most famous mathematical programs in calculating mathematical problems .The aims of this study is to calculate Maxwell’s equations using Matlab .We followed the applied mathematical method by using Matlab .We found that the solution of Matlab is more accuracy and speed than the analytical solution.

scholarly journals EXPONENTIAL CONVERGENCE OF hp-FEM FOR MAXWELL EQUATIONS WITH WEIGHTED REGULARIZATION IN POLYGONAL DOMAINS

2005 ◽  
Vol 15 (04) ◽  
pp. 575-622 ◽  
Author(s):  
MARTIN COSTABEL ◽  
MONIQUE DAUGE ◽  
CHRISTOPH SCHWAB
Keyword(s):  
Finite Element ◽  
Maxwell’S Equations ◽  
Maxwell Equations ◽  
Maxwell's Equations ◽  
Convergence Rates ◽  
Exponential Convergence ◽  
Polygonal Domains ◽  
Time Harmonic ◽  
Standard Tool ◽  
Optimal Convergence Rates

The time-harmonic Maxwell equations do not have an elliptic nature by themselves. Their regularization by a divergence term is a standard tool to obtain equivalent elliptic problems. Nodal finite element discretizations of Maxwell's equations obtained from such a regularization converge to wrong solutions in any non-convex polygon. Modification of the regularization term consisting in the introduction of a weight restores the convergence of nodal FEM, providing optimal convergence rates for the h version of finite elements. We prove exponential convergence of hp FEM for the weighted regularization of Maxwell's equations in plane polygonal domains provided the hp-FE spaces satisfy a series of axioms. We verify these axioms for several specific families of hp finite element spaces.

The symmetrization of Maxwell's equations, and fractionally charged particles

1970 ◽  
Vol 48 (3) ◽  
pp. 279-282 ◽  
Author(s):  
Darryl Leiter
Keyword(s):  
Electric Charge ◽  
Maxwell’S Equations ◽  
Maxwell Equations ◽  
Maxwell's Equations ◽  
Charged Particles ◽  
Charge Ratio ◽  
Model Universe ◽  
Electromagnetic Interactions ◽  
Electromagnetic Tensor ◽  
Classical Point

It is shown that Maxwell's equations can be consistently symmetrized by the introduction of an additional vector 4-current as the source of the dual of the generalized electromagnetic tensor. The additional 4-current is related to a second type of electric charge which we shall call "m-electric charge," as distinguished from the conventional electric charge (denoted as "e-electric" charge). A Lagrangian formulation of this theory for classical point charges is constructed, yielding the symmetrized Maxwell equations, in which each particle is assumed to carry both an "e-electric" charge and an "m-electric" charge. We show that if the m-electric to e-electric charge ratio is the same for all particles in the model universe, then the predictions of the symmetrized Maxwell equations are the same as that of the unsymmetrized, conventional Maxwell equations. However, if all particles in a detector carry the same m-electric to e-electric charge ratio, not equal to zero, then a detected particle with different m-electric to e-electric charge ratio (than that of the detector) could appear to have only a fractional e-electric charge. This implies that fractionally charged particles could be generated even if only integral multiples of e-charge and m-charge were allowed in the symmetrized theory. This means that it might be experimentally difficult to distinguish between a differently "m-charged" particle, and an SU3-type "quark," in purely electromagnetic interactions alone.

scholarly journals Modified Splitting FDTD Methods for Two-Dimensional Maxwell’s Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Liping Gao ◽  
Shouhui Zhai
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell Equations ◽  
Maxwell's Equations ◽  
Scattering Problem ◽  
Fdtd Method ◽  
Second Order ◽  
Numerical Dispersion ◽  
Two Dimensional ◽  
Fourier Methods ◽  
Fdtd Methods

In this paper, we develop a new method to reduce the error in the splitting finite-difference method of Maxwell’s equations. By this method two modified splitting FDTD methods (MS-FDTDI, MS-FDTDII) for the two-dimensional Maxwell equations are proposed. It is shown that the two methods are second-order accurate in time and space and unconditionally stable by Fourier methods. By energy method, it is proved that MS-FDTDI is second-order convergent. By deriving the numerical dispersion (ND) relations, we prove rigorously that MS-FDTDI has less ND errors than the ADI-FDTD method and the ND errors of ADI-FDTD are less than those of MS-FDTDII. Numerical experiments for computing ND errors and simulating a wave guide problem and a scattering problem are carried out and the efficiency of the MS-FDTDI and MS-FDTDII methods is confirmed.

IMPROVEMENT OF MAXWELL'S EQUATIONS IN ORDER TO OBTAIN THE RELATION OF ELECTROMAGNETIC AND GRAVITATIONAL FORCES IN ACCORDANCE WITH THE SRT AND GRT OF EINSTEIN

2020 ◽  
Author(s):  
Андрей Владимирович Рысин ◽  
Игорь Кронидович Никифоров
Keyword(s):  
Quantum Mechanics ◽  
Maxwell’S Equations ◽  
Maxwell Equations ◽  
Maxwell's Equations ◽  
Space Time ◽  
Gravitational Forces ◽  
Time Continuum

Необходимость появления усовершенствованных уравнений Максвелла связано с имеющими место алогизмами и парадоксами вывода ряда уравнений и утверждений в ныне принятой электродинамике и квантовой механике. Основой предложенного авторами подхода является пространственно-временной континуум по преобразованиям Лоренца-Минковского вкупе с электромагнитным континуумом на основе классических уравнений Максвелла. The need for the appearance of improved Maxwell's equations is related to the existing alogisms and paradoxes of the derivation of a number of equations and statements in the currently accepted electrodynamics and quantum mechanics. The approach proposed by the authors is based on the space-time continuum based on Lorentz-Minkowski transformations together with the electromagnetic continuum based on the classical Maxwell equations.

scholarly journals NUMERICAL ANALYSIS OF THE GENERALIZED MAXWELL EQUATIONS (WITH AN ELLIPTIC CORRECTION) FOR CHARGED PARTICLE SIMULATIONS

2009 ◽  
Vol 19 (11) ◽  
pp. 1959-1994 ◽  
Author(s):  
PATRICK CIARLET ◽  
SIMON LABRUNIE
Keyword(s):  
Charged Particle ◽  
Numerical Analysis ◽  
Maxwell’S Equations ◽  
Maxwell Equations ◽  
Continuity Equation ◽  
Maxwell's Equations ◽  
Numerical Solutions ◽  
Well Posedness ◽  
Particle Simulations ◽  
Well Posed

When computing numerical solutions to the Vlasov–Maxwell equations, the source terms in Maxwell's equations usually fail to satisfy the continuity equation. Since this condition is required for the well-posedness of Maxwell's equations, it is necessary to introduce generalized Maxwell's equations which remain well-posed when there are errors in the sources. These approaches, which involve a hyperbolic, a parabolic and an elliptic correction, have been recently analyzed mathematically. The goal of this paper is to carry out the numerical analysis for several variants of Maxwell's equations with an elliptic correction.

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