相关论文: A Two-Step Formulation of Maxwell's Equations Usin…

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…

Model order reduction methods are a powerful tool to drastically reduce the computational effort of problems which need to be evaluated repeatedly, i.e., when computing the same system for various parameter values. When applying a reduced…

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…

A new formulation of the Maxwell equations based on two vector and two scalar potentials is proposed. The use of these potentials allows the electromagnetic field equations to be written in the form of a hyperbolic system. In contrast to…

This paper proposes a finite element method for solving the periodic steady-state problem for the scalar-valued and vector-valued Poisson equations, a simple reduction model of the Maxwell equations under the Coulomb gauge. Introducing a…

This work, that is devoted to the memory of Dr. Andrew Chubykalo and his legacy, is the improved version of the paper published in Annales de la Fondation Louis de Broglie journal. In this article, methods for solving the Maxwell equations…

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 magnetostatics and eddy current problems, formulated in terms of the magnetic vector potential, the solution is not unique, because the addition of an irrotational function to the solution remains a valid solution. The tree-cotree…

In this paper, the stabilized finite element approximation of the Stokes eigenvalue problems is considered for both the two-field (displacement-pressure) and the three-field (stress-displacement-pressure) formulations. The method presented…

The gauge-theoretical method introduced in our previous paper is applied to solve the axisymmetric and static Einstein-Maxwell equations. We obtain the solutions of the non-Weyl class, where the gravitational and electric or magnetic…

We develop a moment equation closure minimization method for the inexpensive approximation of the steady state statistical structure of nonlinear systems whose potential functions have bimodal shapes and which are subjected to correlated…

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…

A new formulation of electromagnetism based on linear differential commutator brackets is developed. Maxwell equations are derived, using these commutator brackets, from the vector potential $\vec{A}$, the scalar potential $\phi$ and the…

Vector and scalar potential formulation is valid from quantum theory to classical electromagnetics. The rapid development in quantum optics calls for electromagnetic solutions that straddle quantum physics as well as classical physics. The…

When simulating resistive-capacitive circuits or electroquasistatic problems where conductors and insulators coexist, one observes that large time steps or low frequencies lead to numerical instabilities, which are related to the condition…

We present a new stabilization technique for multiscale convection diffusion problems. Stabilization for these problems has been a challenging task, especially for the case with high Peclet numbers. Our method is based on a constraint…

The Maxwell equations for the electromagnetic potential, supplemented by the Lorenz gauge condition, are decoupled and solved exactly in de Sitter space-time studied in static spherical coordinates. There is no source besides the…

It is known that with restrictions on the type of the constitutive equations, Maxwell's equations in non-uniform media can sometimes be reduced to two 2nd order differential equations for 2 scalar quantities only. These results have…

In this paper we give a solution formula for the two-phase Stokes equations with and without surface tension and gravity in the whole space with flat interface. The solution formula has already considered by Shibata-Shimizu. However we…

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…