Related papers: An Approach to Maxwell Equations in Uniformly Acce…
In this paper two types of multgrid methods, i.e., the Rayleigh quotient iteration and the inverse iteration with fixed shift, are developed for solving the Maxwell eigenvalue problem with discontinuous relative magnetic permeability and…
This work studies the problem of maximizing a higher degree real homogeneous multivariate polynomial over the unit sphere. This problem is equivalent to finding the leading eigenvalue of the associated symmetric tensor of higher order,…
This paper develops a method for solving Einstein's equation numerically on multi-cube representations of manifolds with arbitrary spatial topologies. This method is designed to provide a set of flexible, easy to use computational…
A Morley-Wang-Xu (MWX) element method with a simply modified right hand side is proposed for a fourth order elliptic singular perturbation problem, in which the discrete bilinear form is standard as usual nonconforming finite element…
Stochastic-periodic homogenization is studied for the Maxwell equations with nonlinear and periodic electric conductivity. It is shown by the stochastic-two-scale convergence method that the sequence of solutions of a class of highly…
We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial…
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…
We develop an advanced method of solving homogeneous and inhomogeneous Bethe-Salpeter equations by using the expansion over the complete set of 4-dimensional spherical harmonics. We solve Bethe-Salpeter equations for bound and scattering…
In this paper, we develop a new type of accelerated algorithms to solve some classes of maximally monotone equations as well as monotone inclusions. Instead of using Nesterov's accelerating approach, our methods rely on a so-called…
Three new iteration methods, namely the squared-operator method, the modified squared-operator method, and the power-conserving squared-operator method, for solitary waves in general scalar and vector nonlinear wave equations are proposed.…
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 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…
In this work numerical methods for solving Einstein's equations are developed and applied to the study of inhomogeneous cosmological models. A two-dimensional computer code is described which implements two advanced numerical methods:…
We investigate a class of localized, stationary, particular numerical solutions to the Maxwell-Dirac system of classical nonlinear field equations. The solutions are discrete energy eigenstates bound predominantly by the self-produced…
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…
Semi-discrete and fully discrete mixed finite element methods are considered for Maxwell-model-based problems of wave propagation in linear viscoelastic solid. This mixed finite element framework allows the use of a large class of existing…
Recently a new formalism for perturbations of Maxwell's equations on the background of the Kerr-NUT-(A)dS spacetime was proposed, with which the equations are reduced to a equation of motion of a scalar field that can be solved by…
The Neumann--Neumann method is a commonly employed domain decomposition method for linear elliptic equations. However, the method exhibits slow convergence when applied to semilinear equations and does not seem to converge at all for…
This paper examines a number of extrapolation and acceleration methods, and introduces a few modifications of the standard Shanks transformation that deal with general sequences. One of the goals of the paper is to lay out a general…
In this paper numerical methods for solving stochastic differential equations with Markovian switching (SDEwMSs) are developed by pathwise approximation. The proposed family of strong predictor-corrector Euler-Maruyama methods is designed…