Related papers: Computation of Maxwell's equations on Manifold usi…
The Duffin-Kemmer form of massless vector field (Maxwell field) is extended to the case of arbitrary pseudo-Riemannian space-time in accordance with the tetrad recipe of Tetrode-Weyl-Fock-Ivanenko. In this approach, the Maxwell equations…
A new algorithm for simulating compact U(1) lattice gauge theory in three dimensions is presented which is based on global changes in the configuration space. We show that this algorithm provides an effective way to extract partition…
We apply topological methods to obtain global continuation results for harmonic solutions of some periodically perturbed ordinary differential equations on a $k$-dimensional differentiable manifold $M \subseteq \mathbb{R}^m$. We assume that…
We present a mimetic finite-difference approach for solving Maxwell's equations in one and two spatial dimensions. After introducing the governing equations and the classical Finite-Difference Time-Domain (FDTD) method, we describe mimetic…
This paper is devoted to the numerical validation of an explicit finite-difference scheme for the integration in time of Maxwell's equations in terms of the sole electric field, using standard linear finite elements for the space…
This paper formulates a new particle-in-cell method for the Vlasov-Maxwell system. Under the Lorenz gauge condition, Maxwell's equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The…
We prove that in contrast to the free wave equation in $\R^3$ there are no incoming solutions of Maxwell's equations in the form of spherical or modulated spherical waves. We construct solutions which are corrected by lower order incoming…
We recommended consequent discrete combinatorial research in mathematical physics. Here we show an example how discretization of partial differential equations can be done and that quickly unexpected new findings can result from research in…
Simulating electromagnetic fields across broad frequency ranges is challenging due to numerical instabilities at low frequencies. This work extends a stabilized two-step formulation of Maxwell's equations to the time-domain. Using a…
The Maxwell equations for the spherical components of the electromagnetic fields outside sources do not separate into equations for each component alone. We show, however, that general solutions can be obtained by separation of variables in…
The Maxwell equations with accounting for tensors properties of time have been considered. The effects that follow from such consideration are described. These are the appearance of vacuum polarization, anisotropy of electromagnetic wave…
The problem of solving partial differential equations (PDEs) on manifolds can be considered to be one of the most general problem formulations encountered in computational multi-physics. The required covariant forms of balance laws as well…
We design in this work a discrete de Rham complex on manifolds. This complex, written in the framework of exterior calculus, has the same cohomology as the continuous de Rham complex, is of arbitrary order of accuracy and, in principle, can…
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…
The scattering of electromagnetic waves by an obstacle is analyzed through a set of partial differential equations combining the Maxwell's model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be…
We express Maxwell's equations as a single equation, first using the divergence of a special type of matrix field to obtain the four current, and then the divergence of a special matrix to obtain the Electromagnetic field. These two…
We discuss umbral calculus as a method of systematically discretizing linear differential equations while preserving their point symmetries as well as generalized symmetries. The method is then applied to the Schr\"{o}dinger equation in…
An efficient numerical solver for the A-Phi formulation in electromagnetics based on the discrete exterior calculus (DEC) is proposed in this paper. The A-Phi formulation is immune to low-frequency breakdown and ideal for broadband and…
A novel approach to computing time-harmonic solutions of Maxwell's equations by time-domain simulations is presented. The method, EM-WaveHoltz, results in a positive definite system of equations which makes it amenable to iterative solution…
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…