Abstract In the last two academical years, as part of the Italian Ministry plan PLS – “Piano Lauree Scientifiche” (Scientific Degree Plan), two courses for high school students and teachers ...consisting in some interdisciplinary and transversal online meetings have been proposed. They regarded the three principles of dynamics, the law of universal gravitation and Maxwell’s equations. “Variations” around these topics were also presented – of historical, philosophical and also of musical nature – to make the cultural setting of what has been discussed deeper and make it meaningful in the present. At the end of each course, students produced a video of few minutes with a personal reworking and rethinking of the meaning of one of the topics discussed.
In this paper, a 3-D hybrid Maxwell's equations finite-difference time-domain (ME-FDTD)/wave equation based finite element time-domain (WE-FETD) method is proposed. This method retains the ...non-conformal mesh and the implicit-explicit time integration scheme. The WE-FETD region is based on the wave equation rather than the Maxwell's curl equations. This method needs to store all the electric fields in the entire region and only the magnetic fields on the interface, which can prominently reduce degrees of freedom (DoFs) and save calculation time. The ME-FDTD region follows the Yee's scheme. A Maxwell's equations spectral element time-domain (ME-SETD) region and a virtual region are used to combine the ME-FDTD and WE-FETD regions. Consequently, a WE-FETD/ME-SETD/Virtual/ME-FDTD framework is formed. Hybrid Newmark-beta (NB) and Crank-Nicolson (CN) time stepping are employed for implicit WE-FETD and ME-SETD regions. The leapfrog (LF) time integration is used for the explicit Virtual and FDTD regions. At the interface, it employs upwind flux in the discontinuous Galerkin (DG) method to couple neighboring regions. Numerical examples are included to demonstrate the accuracy of the proposed method. Several cases exhibit the improved efficiency compared with the hybrid FDTD/FETD method only based on the Maxwell's equations and the pure FETD method.
The time-harmonic Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental for the simulation of many modern devices we have become used to in everyday life. ...The numerical solution of these equations is hampered by two fundamental problems: first, in the high frequency regime, very fine meshes need to be used in order to avoid the pollution effect well known for the Helmholtz equation, and second the large scale systems obtained from the vector valued equations in three spatial dimensions need to be solved by iterative methods, since direct factorizations are not feasible any more at that scale. As for the Helmholtz equation, classical iterative methods applied to discretized Maxwell equations have severe convergence problems.
We explain in this paper a family of domain decomposition methods based on well chosen transmission conditions. We show that all transmission conditions proposed so far in the literature, both for the first and second order formulation of Maxwell's equations, can be written and optimized in the common framework of optimized Schwarz methods, independently of the first or second order formulation one uses, and the performance of the corresponding algorithms is identical. We use a decomposition into transverse electric and transverse magnetic fields to describe these algorithms, which greatly simplifies the convergence analysis of the methods. We illustrate the performance of our algorithms with large scale numerical simulations.
In the current report, wave propagation analysis of a sandwich doubly curved nanopanel considering a laminated composite core and a couple of face sheets of magneto-electro-elastic (MEE) in the ...framework of nonlocal strain gradient theory (NSGT) is investigated. The higher-order-shear-deformable (HSD) model is employed to obtain the formulation of strain-stress equations. Maxwell equations are employed for modeling the behaviors of MEE materials. By considering Hamiltonian, the current model's governing equations have been extracted. Afterward, in order to analyze the influence of wavenumber, inserted ampere, inserted voltage, the laminated structure's geometry, nano-sized mechanics impact on the smart sandwich nano-scaled panel's phase velocity, a parametric study has been considered. It is also observed that by raising the electric potential, the number of critical waves could be likely to be increased. A useful suggestion of this study is that the influence of the magnetic field on the phase velocity is more than the influence of the electric field of the MEE panel on the wave propagation of the smart panel. Besides, the nonlocal parameter and phase velocity have an exponential negative relation, while the length scale parameter and phase velocity have a linear direct relation.
We present several high-order accurate finite element methods for the Maxwell’s equations which provide time-invariant, non-drifting approximations to the total electric and magnetic charges, and to ...the total energy. We devise these methods by taking advantage of the Hamiltonian structures of the Maxwell’s equations as follows. First, we introduce spatial discretizations of the Maxwell’s equations using mixed finite element, discontinuous Galerkin, and hybridizable discontinuous Galerkin methods to obtain a semi-discrete system of equations which display discrete versions of the Hamiltonian structure of the Maxwell’s equations. Then we discretize the resulting semi-discrete system in time by using a symplectic integrator. This ensures the conservation properties of the fully discrete system of equations. For the Symplectic Hamiltonian HDG method, we present numerical experiments which confirm its optimal orders of convergence for all variables and its conservation properties for the total linear and angular momenta, as well as the total energy. Finally, we discuss the extension of our results to other boundary conditions and to numerical schemes defined by different weak formulations.
•A new HDG method for the electric field and magnetic vector potential formulation of Maxwell’s equations.•The first symplectic Hamiltonian hybridizable discontinuous Galerkin method for Maxwell’s equations.•Energy-conserving Mixed, Discontinuous Galerkin and Hybridizable Discontinuous Galerkin methods.•A comprehensive analysis of the Hamiltonian structures of Mixed, DG, and HDG methods for Maxwell’s equations.
This article presents explicit exponential integrators for stochastic Maxwell's equations driven by both multiplicative and additive noises. By utilizing the regularity estimate of the mild solution, ...we first prove that the strong order of the numerical approximation is 12 for general multiplicative noise. Combining a proper decomposition with the stochastic Fubini's theorem, the strong order of the proposed scheme is shown to be 1 for additive noise. Moreover, for linear stochastic Maxwell's equation with additive noise, the proposed time integrator is shown to preserve exactly the symplectic structure, the evolution of the energy as well as the evolution of the divergence in the sense of expectation. Several numerical experiments are presented in order to verify our theoretical findings.
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 multi-symplectic conservation law), and the energy of system is a conservative quantity almost surely. We propose a stochastic multi-symplectic energy-conserving method for the equations by using the wavelet collocation method in space and stochastic symplectic method in time. Numerical experiments are performed to verify the excellent abilities of the proposed method in providing accurate solution and preserving energy. The mean square convergence result of the method in temporal direction is tested numerically, and numerical comparisons with finite difference method are also investigated.
Quantum spin Hall effect of light Bliokh, Konstantin Y.; Smirnova, Daria; Nori, Franco
Science (American Association for the Advancement of Science),
06/2015, Letnik:
348, Številka:
6242
Journal Article
Recenzirano
Odprti dostop
Maxwell's equations, formulated 150 years ago, ultimately describe properties of light, from classical electromagnetism to quantum and relativistic aspects. The latter ones result in remarkable ...geometric and topological phenomena related to the spin-1 massless nature of photons. By analyzing fundamental spin properties of Maxwell waves, we show that free-space light exhibits an intrinsic quantum spin Hall effect—surface modes with strong spin-momentum locking. These modes are evanescent waves that form, for example, surface plasmon-polaritons at vacuum-metal interfaces. Our findings illuminate the unusual transverse spin in evanescent waves and explain recent experiments that have demonstrated the transverse spin-direction locking in the excitation of surface optical modes. This deepens our understanding of Maxwell's theory, reveals analogies with topological insulators for electrons, and offers applications for robust spin-directional optical interfaces.
The quasi-static approximation that considers inductive-capacitive-resistive effects is referred to as the Darwin model of Maxwell's equation. However, numerical analysis of the Darwin model is ...computationally expensive on account of large ill-conditioned equations. In this article, we proposed a new model order reduction technique for the Darwin model of Maxwell's equations to drastically reduce the computational cost. In this method, four symmetric non-gauged equations were solved to obtain the basis vectors and avoid solving the non-symmetric equations. The reduced-order model (ROM) was obtained through congruent transformation, and time-domain analysis was performed using the time-difference method. We observed that the symmetric ROM was superior to the asymmetric ROM, in terms of accuracy and stability of the time-domain analysis.
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