We present a parallelized algorithm for solving the time-dependent Vlasov-Maxwell system of equations in the four-dimensional phase space (two spatial and velocity dimensions). One Vlasov equation is solved for every particle species, from which charge and current densities are calculated for the Maxwell equations. The parallelization is divided into two different layers. For the first layer, e...

We investigate some simple finite element discretizations for the axisymmetric Laplace equation and the azimuthal component of the axisymmetric Maxwell equations as well as multigrid algorithms for these discretizations. Our analysis is targeted at simple model problems and our main result is that the standard V-cycle with point smoothing converges at a rate independent of the number of unknown...

In this paper the Maxwell equations in an exterior domain with the generalized impedance boundary conditions of Engquist-N ed elec are considered. The particular form of the assumed boundary conditions can be considered to be a singular perturbation of the Dirichlet boundary conditions. The convergence of the solution of the Maxwell equations with these generalized impedance boundary conditions...

In this paper we prove in a rigorous mathematical way (using the Clifford bundle formalism) that the energies and momenta of two distinct and arbitrary free Maxwell fields (of finite energies and momenta) that are superposed are additive and thus that there is no incompatibility between the principle of superposition of fields and the principle of energy-momentum conservation, contrary to some ...

In this paper, we consider near cloaking for the full Maxwell equations. We extend the method of [5, 6], where the quasi-static limit case and the Helmholtz equation are considered, to electromagnetic scattering problems. We construct very effective near cloaking structures for the electromagnetic scattering problem at a fixed frequency. These new structures are, before using the transformation...

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...

We give a systematic account of the exterior algebra of forms on q-Minkowski space, introducing the q-exterior derivative, q-Hodge star operator, q-coderivative, q-LaplaceBeltrami operator and the q-Lie-derivative. With these tools at hand, we then give a detailed exposition of the q-d’Alembert and q-Maxwell equation. For both equations we present a q-momentum-indexed family of plane wave solut...

Magnetostatic Maxwell equations and the Landau-Lifshitz-Gilbert (LLG) equation are combined to a multiscale method, which allows to extend the problem size of traditional micromagnetic simulations. By means of magnetostatic Maxwell equations macroscopic regions can be handled in an averaged and stationary sense, whereas the LLG allows to accurately describe domain formation as well as magnetiza...

A lattice Boltzmann model for viscoelastic flow simulation is proposed. Elastic effects are taken into account within the framework of a Maxwell model. To test the approach, we estimate the transverse velocity autocorrelation function for a freely evolving system, and find clear manifestations of shear at large frequencies. We then characterize boundary-driven shear waves, and the resonant enha...

The main purpose of this article is to disseminate among a wide audience of physicists a known result, which is available since a couple of years to the cognoscenti of differential forms on manifolds; namely, that charge conservation implies the inhomogeneous Maxwell equations. This is the reciprocal statement of one which is very well known among physicists: charge conservation, written in the...