Related papers: An Approach to Maxwell Equations in Uniformly Acce…
A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies…
This note offers a conceptually straightforward and efficient way to formulate and solve problems in the electromagnetics of moving media based on a representation of Maxwell's equations in terms of differential forms on spacetime together…
We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We…
The Mathisson-Papapetrou-Dixon (MPD) equations for the motion of electrically neutral massive spinning particles are analysed, in the pole-dipole approximation, in an Einstein-Maxwell plane-wave background spacetime. By exploiting the high…
In this paper we present a methodology for increasing the accuracy and accelerating the convergence of numerical methods for solution of Maxwell's equations in the frequency domain by taking into account the be-havior of the electromagnetic…
The main objective of this work, is to show two inequivalent methods to obtain new spherical symmetric solutions of Einstein's Equations with anisotropy in the pressures in isotropic coordinates. This was done inspired by the MGD method,…
This paper concerns the preconditioning technique for discrete systems arising from time-harmonic Maxwell equations with absorptions, where the discrete systems are generated by N\'ed\'elec finite element methods of fixed order on meshes…
This paper proposes and analyzes a new operator splitting method for stochastic Maxwell equations driven by additive noise, which not only decomposes the original multi-dimensional system into some local one-dimensional subsystems, but also…
This paper studies the numerical methods to approximate the solutions for a sort of McKean-Vlasov neutral stochastic differential delay equations (MV-NSDDEs) that the growth of the drift coefficients is super-linear. First, We obtain that…
The discussion of our recent work concerning the vector solution of boundary-value problems in electromagnetism is extended to the case of no azimuthal symmetry by means of the spin-weighted spherical harmonics.
This paper introduces new discretization schemes for time-harmonic Maxwell equations in a connected domain by using the weak Galerkin (WG) finite element method. The corresponding WG algorithms are analyzed for their stability and…
A new Monte-Carlo method for solving linear parabolic partial differential equations is presented. Since, in this new scheme, the particles are followed backward in time, it provides great flexibility in choosing critical points in…
In this paper, we consider the numerical solution of highly-oscillatory Vlasov and Vlasov-Poisson equations with non-homogeneous magnetic field. Designed in the spirit of recent uniformly accurate methods, our schemes remain insensitive to…
In this paper we are concerned with the plane wave method for the discretization of time-harmonic Maxwell's equations in three dimensions. As pointed out in [6], it is difficult to derive a satisfactory L2 error estimate of the standard…
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…
Discrete mechanics is used to present fluid mechanics, fluid-structure interactions, electromagnetism and optical physics in a coherent theoretical and numerical approach. Acceleration considered as an absolute quantity is written as a sum…
We introduce a high-order spline geometric approach for the initial boundary value problem for Maxwell's equations. The method is geometric in the sense that it discretizes in structure preserving fashion the two de Rham sequences of…
We are concerned with the tensor equations whose coefficient tensor is an M-tensor. We first propose a Newton method for solving the equation with a positive constant term and establish its global and quadratic convergence. Then we extend…
We present a variationally separable splitting technique for the generalized-$\alpha$ method for solving parabolic partial differential equations. We develop a technique for a tensor-product mesh which results in a solver with a linear cost…
The generalized Maxwell equations are considered which include an additional gradient term. Such equations describe massless particles possessing spins one and zero. We find and investigate the matrix formulation of the first order of…