In this paper we discuss some unusual and unsuspected relations between Maxwell, Dirac and the Seiberg-Witten equations. First we investigate what is now known as the Maxwell-Dirac equivalence (MDE) of the first kind. Crucial to that proposed equivalence is the possibility of solving for ψ (a representative on a given spinorial frame of a Dirac-Hestenes spinor field) the equation F = ψγ21˜ψ, wh...

We present numerical results relative to the resolution of the time-harmonic Maxwell equations discretized by discontinuous Galerkin methods. First, a numerical study of the convergence of discontinuous Galerkin methods which compares different strategies proposed in the literature for the elliptic Maxwell equations, is performed in the two-dimensional case. We also introduce a Schwarz-type dom...

We discuss Bogomol'nyi equations for general gauge theories (depending on the two Maxwell invariants F µν F µν and˜F µν F µν) coupled to Higgs scalars. By analysing their supersymmetric extension, we explicitly show why the resulting BPS structure is insensitive to the particular form of the gauge Lagrangian: Maxwell, Born-Infeld or more complicated non-polynomial Lagrangians all satisfy the sa...

Discontinuous Galerkin methods are developed for solving the Vlasov–Maxwell system, methods that are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy. Such properties in general are hard to achieve within other numerical method frameworks for simulating the Vlasov–Maxwell system. The proposed scheme employs discontinuous Galerki...

A continuation method is developed for solving the inverse medium scattering problem of time harmonic Maxwell equations in R3. By using multifrequency scattering data, our reconstruction algorithm first employs the Born approximation for an initial guess and proceeds via recursive linearization on the wavenumber k. At each linearization step, one forward and one adjoint state of the Maxwell equ...

Computational electromagnetism is concerned with the numerical study of Maxwell equations. By choosing a discrete Gaussian measure on prism lattice, we use discrete exterior calculus and lattice gauge theory to construct discrete Maxwell equations in vacuum case. We implement this scheme on Java development plateform to simulate the behavior of electromagnetic waves. This work is partially supp...

The aim of this work is to asses the computational performance of a finite element formulation based on nodal elements and the regularized Maxwell equations. We analyze the memory requirements and the condition number of the matrix when the formulation is applied to electromagnetic engineering problems. As a reference, we solve the same problems with the best known finite element formulation ba...

This paper is concerned with the approximation of the time domain Maxwell equations in a dispersive propagation medium by a Discontinuous Galerkin Time Domain (DGTD) method. The Debye model is used to describe the dispersive behaviour of the medium. We adapt the locally implicit time integration method from [1] and derive a convergence analysis to prove that the locally implicit DGTD method for...