Related papers: Constraint-preserving hybrid finite element method…
Various applications ranging from spintronic devices, giant magnetoresistance sensors, and magnetic storage devices, include magnetic parts on very different length scales. Since the consideration of the Landau-Lifshitz-Gilbert equation…
We study Maxwell's equations in conducting media with perfectly conducting boundary conditions on Lipschitz domains, allowing rough material coefficients and $L^2$-data. Our first contribution is a direct proof of well-posedness of the…
This paper presents a hybridized formulation for the weak Galerkin mixed finite element method (WG-MFEM) which was introduced and analyzed for second order elliptic equations. The WG-MFEM method was designed by using discontinuous piecewise…
We argue that the classical theory of electromagnetism is based on Maxwell's macroscopic equations, an energy postulate, a momentum postulate, and a generalized form of the Lorentz law of force. These seven postulates constitute the…
We consider that no mean magnetic field exists during this epoch, but that there is a mean magnetic energy associated with large-scale magnetic inhomogeneities. We study the evolution of these inhomogeneities and their influence on the…
This work concerns the design and analysis of a limiting technique that allows the preservation of invariant domains for high-order numerical approximations of nonlinear hyperbolic systems of conservation laws. The method can be applied to…
A quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive and absorbing dielectric medium is developed. The classical Maxwell equations with spatially…
Maxwell's equations are modified to incorporate a scalar field to account for the London's superconductivity. Assuming the electromagnetic field is described by the Klein-Gordon equation, London's equations of superconductivity are then…
In this manuscript we present a novel and efficient numerical method for the compressible viscous and resistive MHD equations for all Mach number regimes. The time-integration strategy is a semi-implicit splitting, combined with a hybrid…
We present a graph-based numerical method for solving hyperbolic systems of conservation laws using discontinuous finite elements. This work fills important gaps in the theory as well as practice of graph-based schemes. In particular, four…
In the standard Lagrangian and Hamiltonian approach to Maxwell's theory the potentials $A^{\mu}$ are taken as the dynamical variables. In this paper I take the electric field $\vec{E}$ and the magnetic field $\vec{B}$ as the the dynamical…
A uniqueness result for the recovery of the electric and magnetic coefficients in the time-harmonic Maxwell equations from local boundary measurements is proven. No special geometrical condition is imposed on the inaccessible part of the…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
A hybrid method for the incompressible Navier--Stokes equations is presented. The method inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods when momentum advection becomes significant, equal-order…
Two Hybridizable Discontinuous Galerkin (HDG) schemes for the solution of Maxwell's equations in the time domain are presented. The first method is based on an electromagnetic diffusion equation, while the second is based on Faraday's and…
We consider linear, hyperbolic systems of balance laws in several space dimensions. They possess non-trivial steady states, which result from the equilibrium between derivatives of the unknowns in different directions, and the sources.…
This paper discusses and analyses two domain decomposition approaches for electromagnetic problems that allow the combination of domains discretised by either N\'ed\'elec-type polynomial finite elements or spline-based isogeometric…
We develop arbitrarily high-order, stationarity-preserving stabilized finite element methods for multidimensional nonlinear hyperbolic balance laws on Cartesian grids. We aim at approximating all the steady states of the problem at hand,…
It is shown that the set of equations known as Maxwell's equations perfectly describe two very different systems: (1) the usual electromagnetic phenomena in vacuum or in the matter and (2) the deformation of isotropic solid lattices,…
One way of improving the behavior of finite element schemes for classical, time-dependent Maxwell's equations, is to render them from their hyperbolic character to elliptic form. This paper is devoted to the study of the stabilized linear…