A Non-iterative Hyperbolic, First-order Conservation Law Approach to Divergence-free Solutions to Maxwell's Equations

2015 ◽  
Author(s):  
Richard J. Thompson ◽  
Trevor M. Moeller
Keyword(s):  
Conservation Law ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
First Order ◽  
Divergence Free

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 Stability of a Leap-Frog Discontinuous Galerkin Method for Time-Domain Maxwell's Equations in Anisotropic Materials

2017 ◽  
Vol 21 (5) ◽  
pp. 1350-1375 ◽  
Author(s):  
Adérito Araújo ◽  
Sílvia Barbeiro ◽  
Maryam Khaksar Ghalati
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Mesh Size ◽  
Element Space ◽  
First Order ◽  
Balance Accuracy ◽  
The Stability

AbstractIn this work we discuss the numerical discretization of the time-dependent Maxwell's equations using a fully explicit leap-frog type discontinuous Galerkin method. We present a sufficient condition for the stability and error estimates, for cases of typical boundary conditions, either perfect electric, perfect magnetic or first order Silver-Müller. The bounds of the stability region point out the influence of not only the mesh size but also the dependence on the choice of the numerical flux and the degree of the polynomials used in the construction of the finite element space, making possible to balance accuracy and computational efficiency. In the model we consider heterogeneous anisotropic permittivity tensors which arise naturally in many applications of interest. Numerical results supporting the analysis are provided.

scholarly journals On the Divergenceless Property of the Magnetic Induction Field

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Sergio Severini ◽  
Alessandro Settimi
Keyword(s):  
Magnetic Induction ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Magnetic Monopoles ◽  
Total Momentum ◽  
Necessary Condition ◽  
Induction Field ◽  
Magnetic Induction Field ◽  
Whole Space ◽  
Divergence Free

Maxwell's equations beautifully describe the electromagnetic fields properties. In what follows we will be interested in giving a new perspective to divergence-free Maxwell’s equations regarding the magnetic induction field: ∇·B→(r→,t)=0. To this end we will consider some physical aspects of a system consisting of massive nonrelativistic charged particles, as sources of an electromagnetic field (e.m.) propagating in free space. In particular the link between conservation of total momentum and divergence-free condition for the magnetic induction B→ field will be deeply investigated. This study presents a new context in which the necessary condition for the divergence-free property of the magnetic induction field in the whole space, known as solenoidality condition, directly comes from the conservation of total momentum for the system, that is, sources and field. This work, in general, leads to results that leave some open questions on the existence, or at least the observability, of magnetic monopoles, theoretically plausible only under suitable symmetry assumptions as we will show.

scholarly journals The first and second order equations of the quantum theory

1929 ◽  
Vol 124 (793) ◽  
pp. 143-150 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Quantum Theory ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Electromagnetic Theory ◽  
Second Order ◽  
Electromagnetic Mass ◽  
First Order ◽  
Second Order Equations

The form of the wave equation for a non-rotating electron suggests that it enters into the theory very much in the same way as the wave equation associated with electromagnetic theory. It would be expected to be derivable from equations of the first order corresponding to Maxwell's equations. It has been suggested that the function Ψ might enter by means of a relation such as s = grad Ψ (1) where s replaces the current four vector of the electromagnetic theory. The difficulty in connection with this procedure is to account for the phenomena associated with electronic rotation. Dirac has shown how to overcome this difficulty and has derived first order equations which can be derived from generalisations of Maxwell's equations. There are certain difficulties with regard to the form of Dirac's results which have been much discussed and some of them have been removed. There are two unsatisfactory points in the treatment of this question. One is the introduction of an operator ( h /2 πi ∂/∂ x α - eϕ α ) into the equations when it is desired to pass from a non-electromagnetic problem to one in which an electromagnetic field is present. The second difficulty lies in the occurrence of a term in mc . Darwin has pointed out this difficulty and considers that it is due to our inability to calculate electromagnetic mass in the quantum theory.

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