Related papers: A stabilized Two-Step Formulation of Maxwell's Equ…
This paper presents a new low-frequency stabilization for a two-step formulation solving the full set of Maxwell's equations. The formulation is based on a electric scalar and magnetic vector potential equation using the electroquasistatic…
Maxwell's equations are considered with transparent boundary conditions, for initial conditions and inhomogeneity having support in a bounded, not necessarily convex three-dimensional domain or in a collection of such domains. The numerical…
In this work we discuss the numerical discretization of the time-dependent Maxwell's equations using a fully explicit leap-frog type discontinuous Galerkin method. We present a sufficient condition for the stability, for cases of typical…
In this paper, we propose an accurate numerical means built upon a spectral-Galerkin method in spatial discretization and an enriched multi-step spectral-collocation approach in temporal direction, for Maxwell equations in Cole-Cole…
In this paper we propose and analyze finite element discontinuous Galerkin methods for the one- and two-dimensional stochastic Maxwell equations with multiplicative noise. The discrete energy law of the semi-discrete DG methods were…
We present numerical results concerning the solution of the time-harmonic Maxwell's equations discretized by discontinuous Galerkin methods. In particular, a numerical study of the convergence, which compares different strategies proposed…
We present a higher-order extension of the dual cell method for the time-domain Maxwell equations in three spatial dimensions. The approach builds upon a variational reinterpretation of the Finite Integration Technique on dual meshes and…
In this work, we investigate the propagation of electromagnetic waves in the Cole-Cole dispersive medium by using the discontinuous Galerkin (DG) method to solve the coupled time-domain Maxwell's equations and polarization equation. We…
We present an energy-preserving (either energy-conservative or energy-dissipative) domain of dependence stabilization method for the linear wave equation on cut-cell meshes. Our scheme is based on a standard discontinuous Galerkin…
We present a new algorithm for the discretization of the Vlasov-Maxwell system of equations for the study of plasmas in the kinetic regime. Using the discontinuous Galerkin finite element method for the spatial discretization, we obtain a…
This paper introduces a numerical scheme for time harmonic Maxwell's equations by using weak Galerkin (WG) finite element methods. The WG finite element method is based on two operators: discrete weak curl and discrete weak gradient, with…
The propagation of electromagnetic waves in general media is modeled by the time-dependent Maxwell's partial differential equations (PDEs), coupled with constitutive laws that describe the response of the media. In this work, we focus on…
Time-dependent Maxwell's equations govern electromagnetics. Under certain conditions, we can rewrite these equations into a partial differential equation of second order, which in this case is the vectorial wave equation. For the vectorial…
We consider the numerical discretization of the time-domain Maxwell's equations with an energy-conserving discontinuous Galerkin finite element formulation. This particular formulation allows for higher order approximations of the electric…
We consider a space-time variational formulation of the second-order wave equation, where integration by parts is also applied with respect to the time variable. Conforming tensor-product finite element discretisations with piecewise…
We consider the discretization of electromagnetic wave propagation problems by a discontinuous Galerkin Method based on Trefftz polynomials. This method fits into an abstract framework for space-time discontinuous Galerkin methods for which…
When solving time-dependent hyperbolic conservation laws on cut cell meshes one has to overcome the small cell problem: standard explicit time stepping is not stable on small cut cells if the time step is chosen with respect to larger…
Wave propagation problems for heterogeneous media are known to have many applications in physics and engineering. Recently, there has been an increasing interest in stochastic effects due to the uncertainty, which may arise from impurities…
An hyperelastic biphasic model is presented. For slow-draining problems (permeability less than 1\times10-2 mm4 N-1 s-1), numerical instabilities in the form of non-physical oscillations in the pressure field are observed in 3D problems…
We present a full space-time numerical solution of the advection-diffusion equation using a continuous Galerkin finite element method on conforming meshes. The Galerkin/least-square method is employed to ensure stability of the discrete…