Related papers: Energy-Conserving Hermite Methods for Maxwell's Eq…
In this work, we introduce a novel Hermite method to handle Maxwell's equations for nonlinear dispersive media. The proposed method achieves high-order accuracy and is free of any nonlinear algebraic solver, requiring solving instead small…
Arbitrary order dissipative and conservative Hermite methods for the scalar wave equation achieving $\mathcal{O}(2m)$ orders of accuracy using $\mathcal{O}(m^d)$ degrees of freedom per node in $d$ dimensions are presented. Stability and…
In this paper, a novel sixth order energy-conserved method is proposed for solving the three-dimensional time-domain Maxwell's equations. The new scheme preserves five discrete energy conservation laws, three momentum conservation laws,…
We present two strategies for designing passivity preserving higher order discretization methods for Maxwell's equations in nonlinear Kerr-type media. Both approaches are based on variational approximation schemes in space and time. This…
We present an energy-conserving numerical scheme to solve the Vlasov-Maxwell (VM) system based on the regularized moment method proposed in [Z. Cai, Y. Fan, and R. Li. CPAM, 2014]. The globally hyperbolic moment system is deduced for the…
Hermite methods, as introduced by Goodrich et al., combine Hermite interpolation and staggered (dual) grids to produce stable high order accurate schemes for the solution of hyperbolic PDEs. We introduce three variations of this Hermite…
The Hermite-Taylor method evolves all the variables and their derivatives through order $m$ in time to achieve a $2m+1$ order rate of convergence. The data required at each node of the staggered Cartesian meshes used by this method makes…
We propose a multi-moment method for one-dimensional hyperbolic equations with smooth coefficient and piecewise constant coefficient. The method is entirely based on the backward characteristic method and uses the solution and its…
In this paper, it is shown that three-dimensional stochastic Maxwell equations with multiplicative noise are stochastic Hamiltonian partial differential equations possessing a geometric structure (i.e. stochastic mutli-symplectic…
Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an…
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…
We describe a fourth-order accurate finite-difference time-domain scheme for solving dispersive Maxwell's equations with nonlinear multi-level carrier kinetics models. The scheme is based on an efficient single-step three time-level…
We develop a finite volume method for Maxwell's equations in materials whose electromagnetic properties vary in space and time. We investigate both conservative and non-conservative numerical formulations. High-order methods accurately…
We present a Hermite interpolation based partial differential equation solver for Hamilton-Jacobi equations. Many Hamilton-Jacobi equations have a nonlinear dependency on the gradient, which gives rise to discontinuities in the derivatives…
The aim of this article is to investigate the well-posedness, stability and convergence of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings. The situation we…
We study the systematic numerical approximation of Maxwell's equations in dispersive media. Two discretization strategies are considered, one based on a traditional leapfrog time integration method and the other based on convolution…
We study a system of Maxwell's equations that describes the time evolution of electromagnetic fields with an additional electric scalar variable to make the system amenable to a mixed finite element spatial discretization. We demonstrate…
We study the conservation properties of the Hermite-discontinuous Galerkin (Hermite-DG) approximation of the Vlasov-Maxwell equations. In this semi-discrete formulation, the total mass is preserved independently for every plasma species.…
For the Maxwell's equations in a Havriliak-Negami (H-N) dispersive medium, the associated energy dissipation law has not been settled at both continuous level and discrete level. In this paper, we rigorously show that the energy of the H-N…
High order accurate Hermite methods for the wave equation on curvilinear domains are presented. Boundaries are treated using centered compatibility conditions rather than more standard one-sided approximations. Both first-order-in-time…