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A STOCHASTIC GALERKIN METHOD FOR maxwell equations WITH UNCERTAINTY

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Acta Mathematica Scientia 2020年第4期40卷 1091-1104页

作者： Lizheng CHENG Bo WANG Ziqing XIE LCSM(MOE)and School of Mathem atics and Statistics Hunan Normal UniversityChangsha 410081China Information Science and Engineering College Hunan International Economics UniversityChangsha 410205China

In this article,we investigate a stochastic Galerkin method for the maxwell equations with random *** generalized Polynomial Chaos(gPC)expansion technique is used to obtain a deterministic system of the gPC expansion *** regularity of the solution with respect to the random is *** the basis of the regularity results,the optimal convergence rate of the stochastic Galerkin approach for maxwell equations with random inputs is *** examples are presented to support the theoretical analysis.

关键词： maxwell equations random inputs stochastic Galerkin method gPC expansion convergence analysis

Effective maxwell equations from Time-dependent Density Functional Theory

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Acta Mathematica Sinica,English Series 2011年第2期27卷 339-368页

作者： Weinan E Jianfeng LU Xu YANG Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA Beijing International Center for Mathematical Research and School of Mathematical Sciences Peking University Beijing 100871 P. R. China Department of Mathematics Courant Institute of Mathematical Sciences New York University New York NY 10012 USA

The behavior of interacting electrons in a perfect crystal under macroscopic external electric and magnetic fields is studied. Effective maxwell equations for the macroscopic electric and magnetic fields are derived starting from time-dependent density functional theory. Effective permittivity and permeability coefficients are obtained.

关键词： Time-dependent density functional theory maxwell equations effective permittivity electromagnetic fields

f(R) gravity and maxwell equations from the holographic principle

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Science China(Physics,Mechanics & Astronomy) 2012年第3期55卷 375-380页

作者： MIAO RongXin MENG Jun LI Miao Interdisciplinary Center for Theoretical Study University of Science and Technology of ChinaHefei 230026China Kavli Institute for Theoretical Physics Key Laboratory of Frontiers in Theoretical PhysicsInstitute of Theoretical PhysicsChinese Academy of SciencesBeijing 100190China

Extending the holographic program of our previous work,we derive f(R) gravity and the maxwell equations from the holographic principle,using time-like holographic *** find that to derive the Einstein equations and f(R) gravity by a natural holographic approach,the quasi-static condition is *** also find the surface stress tensor and the surface electric current,surface magnetic current on a holographic screen for f(R) gravity and maxwell's theory,respectively.

关键词： entropic gravity f(R) gravity maxwell equations the holographic principle

STABILITY AND SUPER CONVERGENCE ANALYSIS OF ADI-FDTD FOR THE 2D maxwell equations IN A LOSSY MEDIUM

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Acta Mathematica Scientia 2012年第6期32卷 2341-2368页

作者：高理平 Department of Computational and Applied Mathematics School of SciencesChina University of Petroleum

Several new energy identities of the two dimenslonal（2D） maxwell equations in a lossy medium in the case of the perfectly electric conducting boundary conditions are proposed and proved. These identities show a new kind of energy conservation in the maxwell system and provide a new energy method to analyze the alternating direction im- plicit finite difference time domain method for the 2D maxwell equations （2D-ADI-FDTD）. It is proved that 2D-ADI-FDTD is approximately energy conserved, unconditionally sta- ble and second order convergent in the discrete L2 and H1 norms, which implies that 2D-ADI-FDTD is super convergent. By this super convergence, it is simply proved that the error of the divergence of the solution of 2D-ADI-FDTD is second order accurate. It is also proved that the difference scheme of 2D-ADI-FDTD with respect to time t is second order convergent in the discrete H1 norm. Experimental results to confirm the theoretical analysis on stability, convergence and energy conservation are presented.

关键词： stability convergence energy conservation ADI-FDTD maxwell equations

A wavelet multiscale method for inversion of maxwell equations

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Applied Mathematics and Mechanics(English Edition) 2009年第8期30卷 1035-1044页

作者：丁亮韩波刘家琦 Department of Mathematics Harbin Institute of Technology

This paper is concerned with estimation of electrical conductivity in maxwell equations. The primary difficulty lies in the presence of numerous local minima in the objective functional. A wavelet multiscale method is introduced and applied to the inversion of maxwell equations. The inverse problem is decomposed into multiple scales with wavelet transform, and hence the original problem is reformulated to a set of sub-inverse problems corresponding to different scales, which can be solved successively according to the size of scale from the shortest to the longest. The stable and fast regularized Gauss-Newton method is applied to each scale. Numerical results show that the proposed method is effective, especially in terms of wide convergence, computational efficiency and precision.

关键词： maxwell equations wavelet Gauss-Newton method finite difference time multiscale method inversion regularized domain method

Stability and superconvergence analysis of the FDTD scheme for the 2D maxwell equations in a lossy medium

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Science China Mathematics 2011年第12期54卷 2693-2712页

作者： GAO LiPing ZHANG Bo Department of Computational and Applied Mathematics School of Sciences China University of Petroleum Qingdao 266555 China LSEC and Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

This paper is concerned with the stability and superconvergence analysis of the famous finite-difference time-domain (FDTD) scheme for the 2D maxwell equations in a lossy medium with a perfectly electric conducting (PEC) boundary condition, employing the energy method. To this end, we first establish some new energy identities for the 2D maxwell equations in a lossy medium with a PEC boundary condition. Then by making use of these energy identities, it is proved that the FDTD scheme and its time difference scheme are stable in the discrete L2 and H1 norms when the CFL condition is satisfied. It is shown further that the solution to both the FDTD scheme and its time difference scheme is second-order convergent in both space and time in the discrete L2 and H1 norms under a slightly stricter condition than the CFL condition. This means that the solution to the FDTD scheme is superconvergent. Numerical results are also provided to confirm the theoretical analysis.

关键词： maxwell equations finite-difference time-domain method stability superconvergence perfectly electric conducting boundary conditions energy identities

GLOBAL SUPERCONVERGENCE OF THE MIXED FINITE ELEMENT METHODS FOR 2-D maxwell equations

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Journal of Computational Mathematics 2003年第5期21卷 637-646页

作者： Jia-fuLin QunLin InstituteofSystemsSciences ChineseAcademyofSciencesBeijing100080China LSEC ICMSECAcademyofMathematicsandSystemSciencesChineseAcademyofSciencesBeijing100080China

Superconvergence of the mixed finite element methods for 2-d maxwell equations is studied in this paper. Two order of superconvergent factor can be obtained for the k-th Nedelec elements on the rectangular meshes.

关键词： maxwell equations Mixed finite element Superconvergence Postprocessing.

maxwell equations and Magnetic Monopoles

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Journal of Applied Mathematics and Physics 2024年第3期12卷 737-763页

作者： Sebastiano Tosto ENEA Rome Italy

The manuscript introduces an “ab initio” quantum model to deduce the maxwell equations. After general considerations and laying out the model’s theoretical framework, these equations can be derived alongside a broad variety of other results. Specifically, a corollary of the present model proposes a possible mechanism underlying the formation of magnetic monopoles and allows estimating their formation energy in order of magnitude.

关键词： “Ab Initio” Quantum Model maxwell equations Theoretical Framework Magnetic Monopoles Formation Energy

EXACT INTERNAL CONTROLLABILITY OF maxwell equations

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EXACT INTERNAL CONTROLLABILITY OF MAXWELL EQUATIONS