In this report, after pedagogical mathematical insight into basic notions of numerical analysis for di erential equations, more speci c Discontinuous Galerkin (DG) method is introduced. Afterwards, the DG method is combined with a fourth-order staggered Leap-Frog (LF4) scheme to be applied to the solution of the Maxwell equations wavepropagation problem. Stability analysis of the resulting sche...

We study the electromagnetic field equations on an arbitrary quantum curved background in the semiclassical approximation of Loop QuantumGravity. The effective interaction hamiltonian for the Maxwell and gravitational fields is obtained and the corresponding field equations, which can be expressed as a modified wave equation for the Maxwell potential, are derived. We use these results to analyz...

A proof of strong cosmic censorship is presented for a class of solutions of the Einstein-Maxwell equations, those with polarized Gowdy symmetry. A key element of the argument is the observation that by means of a suitable choice of variables the central equations in this problem can be written in a form where they are identical to the central equations for general (i.e. non-polarized) vacuum G...

We report what we believe to be the first rigorous numerical solution of the two-dimensional Maxwell equations for optical propagation within, and scattering by, a random medium of macroscopic dimensions. Our solution is based on the pseudospectral time-domain technique, which provides essentially exact results for electromagnetic field spatial modes sampled at the Nyquist rate or better. The r...

There exist different methods to find the solutions of the Einstein–Maxwell equations [1]. Some high symmetry solutions of the Einstein equations have direct astrophysical or cosmological interpretation [2]. In [3], a new conjecture was formulated which says: “ A test electromagnetic field having a potential proportional to the Killing vector of a seed vacuum gravitational field (up to a consta...

SUMMARY In this paper an inverse scattering problem for the time-dependent Maxwell curl equations is considered. This problem is formulated as an optimal control problem governed by partial differential equations. First-order necessary optimality conditions are discussed. For the numerical solution a gradient-based algorithm is applied and successfully tested for some numerical examples. Finall...

MHD flows are governed by the Navier-Stokes equations coupled with the Maxwell equations. Broadly, MHD flows in astrophysics occur at large magnetic Reynolds numbers while those in terrestrial applications, such as liquid metals, occur at small magnetic Reynolds numbers, the case considered herein. The physical processes of fluid flows and electricity and magnetism are quite different and numer...

We present the discretized equations of the 12 PML (perfectly matched layer) in the three-dimensional case using the Cartesian geometry. These equations can be used in different fields where Maxwell equations need to be solved.

The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell’s equations in which charge conservation is emphasized as the fundamental axiom underlying these equations.

In this paper, we are concerned with the Cauchy problem on the compressible isentropic two-fluids Euler-Maxwell equations in three dimensions. The global existence of solutions near constant steady states with the vanishing electromagnetic field is established, and also the time-decay rates of perturbed solutions in L space for 2 ≤ q ≤ ∞ are obtained. The proof for existence is due to the class...