Split-step procedures have previously been used successfully in a number of situations, e.g. for Hamiltonian systems, such as certain nonlinear wave equations. In this study, we note that one particular way to write the 3-D Maxwell’s equations separates these into two parts, requiring in all only the solution of six uncoupled 1-D wave equations. The approach allows arbitrary orders of accuracy ...

The relation between the two most important in mathematical physics first order systems of partial differential equations is among those topics which attract attention because of their general, even philosophical significance but at the same time do not offer much for the solution of particular problems concerning physical models. The Maxwell equations can be represented in a Dirac like form in...

We study and report on the class of vacuum Maxwell fields in Minkowski space that possess a non-degenerate, diverging, principle null vector field (null eigenvector field of the Maxwell tensor) that is tangent to a shear-free null geodesics congruence. These congruences can be either surface forming (the tangent vectors being proportional to gradients) or not, i.e., the twisting congruences. In...

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...

The state of the art for mesh coupling at nonconforming interfaces is presented and reviewed. Mesh coupling is frequently applied to dealing with motion in electromagnetic actuators [1, 2, 3]. The focus of the contribution is on lowest order Whitney elements. Both interpolationand projection-based methods are considered [4]. In addition to accuracy and efficiency, we emphasize the question whet...

In this article we study the existence of infinitely many large energy solutions for the superlinear Schrödinger-Maxwell equations −∆u+ V (x)u+ φu = f(x, u) in R, −∆φ = u, in R, via the Fountain Theorem in critical point theory. In particular, we do not use the classical Ambrosetti-Rabinowitz condition.

We write the Mathisson-Papapetrou equations of motion for a spinning particle in a stationary spacetime using the quasi-Maxwell formalism and give an interpretation of the coupling between spin and curvature.

The factorization method can be applied for certain classes of inverse problems where the shape of a domain has to be determined. It constructs a binary criterion which determines whether a given point is inside or outside the domain. The present paper develops the theory of the factorization method for the time harmonic Maxwell system where the support of the contrast of the index of refractio...

We prove global Hölder regularity for the solutions to the timeharmonic anisotropic Maxwell’s equations, under the assumptions of Hölder continuous coefficients. The regularity hypotheses on the coefficients are minimal. The same estimates hold also in the case of bianisotropic material parameters.

We consider for the time-dependent Maxwell’s equations the inverse problem of identifying locations and certain properties of small electromagnetic inhomogeneities in a homogeneous background medium from dynamic measurements of the tangential component of the magnetic field on the boundary ( or a part of the boundary) of a domain.