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ON DIsCRETE ENERGY DIssIPATION OF maxwell’s equations IN A COLE-COLE DIsPERsIVE MEDIUM

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Journal of Computational Mathematics 2023年第5期41卷 980-1002页

作者： Baoli Yin Yang Liu Hong Li Zhimin Zhang school of Mathematical sciences Inner Mongolia UniversityHohhot 010021China Beijing Computational science Research Center Beijing 100193China Department of Mathematics Wayne State UniversityDetroitMI 48202USA

A simple criterion is studied for the first time for identifying the discrete energy dissipation of the Crank-Nicolson scheme for maxwell’s equations in a Cole-Cole dispersive *** numerical formulas that approximate the time fractional derivatives are investigated based on this criterion,including the L1 formula,the fractional BDF-2,and the shifted fractional trapezoidal rule(sFTR).Detailed error analysis is provided within the framework of time domain mixed finite element methods for smooth *** convergence results and discrete energy dissipation law are confirmed by numerical *** nonsmooth solutions,the method sFTR can still maintain the optimal convergence order at a positive time on uniform *** believe this is the first appearance that a second-order time-stepping method can restore the optimal convergence rate for maxwell’s equations in a Cole-Cole dispersive medium regardless of the initial singularity of the solution.

关键词： Discrete energy dissipation Crank-Nicolson scheme maxwell’s equations shifted fractional trapezoidal rule Mixed finite element methods

Development of an Explicit symplectic scheme that Optimizes the Dispersion-Relation Equation of the maxwell’s equations

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Communications in Computational Physics 2013年第4期13卷 1107-1133页

作者： Tony W.H.sheu L.Y.Liang J.H.Li Department of Engineering science and Ocean Engineering National TaiwanUniversityNo.1Sec.4Roosevelt RoadTaipeiTaiwan Taida Institute of Mathematical science(TIMs) National Taiwan UniversityTaiwan Center for Quantum science and Engineering(CQsE) National Taiwan UniversityTaiwan

In this paper an explicit finite-difference time-domain scheme for solving the maxwell’s equations in non-staggered grids is *** proposed scheme for solving the Faraday’s and Amp`ere’s equations in a theoretical manner is aimed to preserve discrete zero-divergence for the electric and magnetic *** inherent local conservation laws in maxwell’s equations are also preserved discretely all the time using the explicit second-order accurate symplectic partitioned Runge-Kutta *** remaining spatial derivative terms in the semi-discretized Faraday’s and Amp`ere’s equations are then discretized to provide an accurate mathematical dispersion relation equation that governs the numerical angular frequency and the wavenumbers in two space *** achieve the goal of getting the best dispersive characteristics,we propose a fourth-order accurate space centered scheme which minimizes the difference between the exact and numerical dispersion relation *** the computational exercises,the proposed dual-preserving solver is computationally demonstrated to be efficient for use to predict the long-term accurate maxwell’s solutions.

关键词： maxwell’s equations non-staggered grids zero-divergence fourth-order dualpreserving solver dispersion relation equations

Finite Element Analysis of maxwell’s equations in Dispersive Lossy Bi-Isotropic Media

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Advances in Applied Mathematics and Mechanics 2013年第4期5卷 494-509页

作者： Yunqing Huang Jichun Li Yanping Lin Hunan Key Laboratory for Computation and simulation in science and Engineering Xiangtan UniversityHunan 411105China Department of Mathematical sciences University of Nevada Las VegasLas VegasNevada 89154-4020USA Department of AppliedMathematics Hong Kong Polytechnic UniversityHung HomHong Kongand Department of Mathematical and Statistics ScienceUniversity of AlbertaEdmonton ABAlberta T6G 2G1Canada

In this paper,the time-dependent maxwell’s equations used to modeling wave propagation in dispersive lossy bi-isotropic media are *** and uniqueness of the modeling equations are *** fully discrete finite element sch... 详细信息

关键词： maxwell’s equations bi-isotropic media finite element method

A High-OrderDiscontinuous GalerkinMethod for the Two-Dimensional Time-Domain maxwell’s equations on Curved Mesh

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Advances in Applied Mathematics and Mechanics 2016年第1期8卷 104-116页

作者： Hongqiang Lu Yida Xu Yukun Gao Wanglong Qin Qiang sun College of Aerospace Engineering Nanjing University of Aeronautics and AstronauticsNanjing 210016China

In this paper,a DG(Discontinuous Galerkin)method which has been widely employed in CFD(Computational Fluid Dynamics)is used to solve the twodimensional time-domain maxwell’s equations for complex geometries on unstructured *** element interfaces on solid boundary are treated in both curved way and straight *** tests are performed for both benchmark problems and complex cases with varying orders on a series of grids,where the high-order convergence in accuracy can be *** the curved and the straight solid boundary implementation can give accurate RCs(Radar Cross-section)results with sufficiently small mesh size,but the curved solid boundary implementation can significantly improve the accuracy when using relatively large mesh *** importantly,this CFD-based high-order DG method for the maxwell’s equations is very suitable for complex geometries.

关键词： maxwell’s equations discontinuous Galerkin method curved mesh radar crosssection.

Posteriori Error Estimation for an Interior Penalty Discontinuous Galerkin Method for maxwell’s equations in Cold Plasma

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Advances in Applied Mathematics and Mechanics 2009年第1期1卷 107-124页

作者： Jichun Li Department of Mathematical sciences University of NevadaLas VegasNevada 89154USA Institute for Pure and Applied Mathematics(IPAM) Building 460 Portola PlazaBox 957121 University of CaliforniaLos AngelesCA 90095-7121USA

In this paper,we develop a residual-based a posteriori error estimator for the time-dependent maxwell’s equations in the cold *** we consider a semi-discrete interior penalty discontinuous Galerkin(DG)method for solving the governing *** provide both the upper bound and lower bound analysis for the error *** is the first posteriori error analysis carried out for the maxwell’s equations in dispersive media.

关键词： Posteriori error estimator maxwell’s equations cold plasma discontinuous Galerkin method

Adaptive hp-FEM with Arbitrary-Level Hanging Nodes for maxwell’s equations

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Advances in Applied Mathematics and Mechanics 2010年第4期2卷 518-532页

作者： Pavel solin Lenka Dubcova Ivo Dolezel Department of Mathematics and statistics University of NevadaReno89557USA Institute of Thermomechanics Academy of Sciences of the Czech RepublicNarodni 311720 Praha 1Czech Republic

Adaptive higher-order finite element methods(hp-FEM)are well known for their potential of exceptionally fast(exponential)***,most hp-FEM codes remain in an academic setting due to an extreme algorithmic complexity of hp-adaptivity *** paper aims at simplifying hpadaptivity for H(curl)-conforming approximations by presenting a novel technique of arbitrary-level hanging *** technique is described and it is demonstrated numerically that it makes adaptive hp-FEM more efficient compared to hp-FEM on regular meshes and meshes with one-level hanging nodes.

关键词： hp-FEM arbitrary-level hanging nodes irregular meshes higher-order edge elements maxwell’s equations

Multi-symplecticWavelet Collocation Method for maxwell’s equations

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Advances in Applied Mathematics and Mechanics 2011年第6期3卷 663-688页

作者： Huajun Zhu songhe song Yaming Chen Department of Mathematics and system science School of ScienceNational University of Defense TechnologyChangsha 410073China

In this paper,we develop a multi-symplectic wavelet collocation method for three-dimensional(3-D)maxwell’s *** the multi-symplectic formulation of the equations,wavelet collocation method based on autocorrelation functions is applied for spatial discretization and appropriate symplectic scheme is employed for time *** analysis shows that the proposed method is multi-symplectic,unconditionally stable and energy-preserving under periodic boundary *** numerical dispersion relation is *** with splitting scheme,an explicit splitting symplectic wavelet collocation method is also *** experiments illustrate that the proposed methods are efficient,have high spatial accuracy and can preserve energy conservation laws exactly.

关键词： Multi-symplectic wavelet collocation method maxwell’s equations symplectic conservation laws

New Energy-Conserved Identities and super-Convergence of the symmetric EC-s-FDTD scheme for maxwell’s equations in 2D

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Communications in Computational Physics 2012年第5期11卷 1673-1696页

作者： Liping Gao Dong Liang Department of Computational and Applied Mathematics School of SciencesChina University of PetroleumQingdao266555P.R.China Department of Mathematics and statistics York UniversityTorontoOntarioM3J 1P3Canada

The symmetric energy-conserved splitting FDTD scheme developed in[1]is a very new and efficient scheme for computing themaxwell’s *** is based on splitting the whole maxwell’s equations and matching the x-direction and y-direction electric fields associated to the magnetic field *** this paper,we make further study on the scheme for the 2D maxwell’s equations with the PEC boundary *** new energy-conserved identities of the symmetric EC-s-FDTD scheme in the discrete H^(1)-norm are *** is then proved that the scheme is unconditionally stable in the discrete H^(1)-*** the new energy-conserved identities,the super-convergence of the symmetric EC-s-FDTD scheme is further proved that it is of second order convergence in both time and space steps in the discrete H^(1)-*** experiments are carried out and confirm our theoretical results.

关键词： symmetric EC-s-FDTD energy-conserved unconditional stability super convergence maxwell’s equations splitting

Analysis and Application of stochastic Collocation Methods for maxwell’s equations with Random Inputs

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Advances in Applied Mathematics and Mechanics 2018年第6期10卷 1305-1326页

作者： Jichun Li Zhiwei Fang Department of Mathematical sciences University of NevadaLas VegasNevada 89154-4020USA

In this paper we develop and analyze the stochastic collocation method for solving the time-dependent maxwell’s equations with random coefficients and subject to random initial *** provide a rigorous regularity analysis of the solution with respect to the random *** our best knowledge,this is the first theoretical results derived for the standard maxwell’s equations with random *** rate of convergence is proved depending on the regularity of the *** results are presented to confirm the theoretical analysis.

关键词： maxwell’s equations random permittivity and permeability stochastic collocation methods uncertainty quantification