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作者： Chatibi, Youness El Kinani, El Hassan Ouhadan, Abdelaziz Mathematical Modeling and Scientific Computing Team Department of Mathematics National School of Arts and Crafts Moulay Ismail University Meknès Morocco Mathematical and Didactical Research Team Department of Mathematics Regional Center of Education and Training Trades Meknès Morocco

In this paper, the Hydon method to determine discrete symmetries for a differential equation is employed to construct discrete symmetries for a family of ordinary, partial, and fractional differential equations. An application of those discrete symmetries to construct other solutions from known ones is illustrated. © 2019 John Wiley & Sons, Ltd.

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Unconditionally optimal convergence of an energy-conserving and linearly implicit scheme for nonlinear wave equations

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Science China mathematics 2022年第8期65卷 1731-1748页

作者： Waixiang Cao Dongfang Li Zhimin Zhang School of Mathematical Sciences Beijing Normal UniversityBeijing 100875China School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China Beijing Computational Science Research Center Beijing 100193China Department of Mathematics Wayne State UniversityDetroitMI 48202USA

In this paper,we present and analyze an energy-conserving and linearly implicit scheme for solving the nonlinear wave *** error estimates in time and superconvergent error estimates in space are established without certain time-step *** key is to estimate directly the solution bounds in the H-norm for both the nonlinear wave equation and the corresponding fully discrete scheme,while the previous investigations rely on the temporal-spatial error splitting *** examples are presented to confirm energy-conserving properties,unconditional convergence and optimal error estimates,respectively,of the proposed fully discrete schemes.

关键词： scalar auxiliary variable wave equations stability error estimate superconvergence

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High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

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Advances in Aerodynamics 2020年第1期2卷 555-578页

作者： Yanqun Jiang Xun Chen Xu Zhang Tao Xiong Shuguang Zhou Department of Mathematics Southwest University of Science and Technology621010 MianyangChina School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific ComputingXiamen University361005 XiamenChina Computational Aerodynamics Institute China Aerodynamics Research and Development Center621000 MianyangChina

The computation of compressible flows at all Mach numbers is a very challenging *** efficient numerical method for solving this problem needs to have shock-capturing capability in the high Mach number regime,while it can deal with stiffness and accuracy in the low Mach number *** paper designs a high order semi-implicit weighted compact nonlinear scheme(WCNS)for the all-Mach isentropic Euler system of compressible gas *** avoid severe Courant-Friedrichs-Levy(CFL)restrictions for low Mach flows,the nonlinear fluxes in the Euler equations are split into stiff and non-stiff components.A third-order implicit-explicit(IMEX)method is used for the time discretization of the split components and a fifth-order WCNS is used for the spatial discretization of flux *** high order IMEX method is asymptotic preserving and asymptotically accurate in the zero Mach number ***-and two-dimensional numerical examples in both compressible and incompressible regimes are given to demonstrate the advantages of the designed IMEX WCNS.

关键词： High order scheme IMEX time discretization WCNS Asymptotic-preserving property Low Mach number Isentropic Euler equations

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A multidomain legendre pseudospectral frequency-domain method with penalty scheme for solving Maxwell's equations

A multidomain legendre pseudospectral frequency-domain metho...

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International Conference on Applications of Electromagnetism and Student Innovation Competition Awards

作者： Wang, Chih-Yu Chung, Shih-Yung Teng, Chun-Hao Chen, Chung-Ping Chang, Hung-Chun Graduate Institute of Electronics Engineering Department of Electrical Engineering National Taiwan University Taipei 10617 Taiwan Department of Applied Mathematics Center of Mathematical Modeling and Scientific Computing National Chiao Tung University Hsinchu 30010 Taiwan Department of Electrical Engineering Graduate Institute of Photonics and Optoelectronics National Taiwan University Taipei 10617 Taiwan

ISBN: (纸本)9781424464166

A new multidomain pseudospectral frequency-domain (PSFD) method based on Legendre polynomials with a penalty scheme for studying electromagnetic wave scattering is presented. Scattered field calculation with accuracy on the order of 9 10- is obtained for a circular plasmonic cylinder. The method is further applied to demonstrate the scattering by a dielectric rectangular cylinder with sharp corners and by multiple circular plasmonic cylinders. ©2010 IEEE.

关键词： Plasmonics

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Electromagnetic simulations of 2D optical microring resonators using the multidomain legendre pseudospectral time-domain method

Electromagnetic simulations of 2D optical microring resonato...

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International Conference on Applications of Electromagnetism and Student Innovation Competition Awards

作者： Chung, Shih-Yung Wang, Chih-Yu Teng, Chun-Hao Chen, Chung-Ping Chang, Hung-Chun Graduate Institute of Electronics Engineering Department of Electrical Engineering National Taiwan University Taipei 10617 Taiwan Department of Applied Mathematics Center of Mathematical Modeling and Scientific Computing National Chiao Tung University Hsinchu 30010 Taiwan Department of Electrical Engineering Graduate Institute of Photonics and Optoelectronics National Taiwan University Taipei 10617 Taiwan

ISBN: (纸本)9781424464166

The high-accuracy pseudospectral time-domain (PSTD) method is utilized to simulate electromagnetic responses of two-dimensional (2D) optical microring resonators. Besides its inherent spectral convergence in accuracy, the PSTD method using multidomain approach with curvilinear-quadrilateral subdomain partitioning possesses superior advantage in fulfilling field continuity conditions across material interfaces. And it should provide better results than the FDTD method simulations for optical waveguide resonators involving circular rings since the stair-casing approximation as often employed in the latter is avoided. ©2010 IEEE.

关键词： Electromagnetic simulation

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Adaptive energy-preserving algorithms for guiding center system

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Plasma Science and Technology 2023年第4期25卷 11-22页

作者：朱贝贝刘健张嘉炜祝爱卿唐贻发 Department of Applied Mathematics School of Mathematics and PhysicsUniversity of Science and Technology BeijingBeijing 100083Peopleʼs Republic of China School of Nuclear Science and Technology University of Science and Technology of ChinaHefei 230026Peopleʼs Republic of China Advanced algorithm Joint Lab Shandong Computer Science CenterQilu University of TechnologyJinan 250014Peopleʼs Republic of China The State Key Laboratory of Scientific and Engineering Computing The Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190Peopleʼs Republic of China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049Peopleʼs Republic of China

We develop two types of adaptive energy preserving algorithms based on the averaged vector field for the guiding center dynamics,which plays a key role in magnetized *** adaptive scheme is applied to the Gauss Legendre’s quadrature rules and time stepsize respectively to overcome the energy drift problem in traditional energy-preserving *** new adaptive algorithms are second order,and their algebraic order is carefully *** results show that the global energy errors are bounded to the machine precision over long time using these adaptive algorithms without massive extra computation cost.

关键词： guiding center system energy-preserving methods adaptive energy conservation

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Hyperbolic Problems: Theory, Numerics, Applications 1

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1000年

作者： Thomas Y. Hou Eitan Tadmor

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Laboratory Study of Different Social Groups Behavior during the Pandemic 13

Laboratory Study of Different Social Groups Behavior during ...

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13th International Conference Management of Large-Scale System Development, MLSD 2020

作者： Gezha, Vlad Menshikova, Olga Sedush, Anna Yaminov, Rinat Zarubin, Ilya Moscow Institute of Physics and Technology Department of Control and Applied Mathematics Dolgoprudny Russia Russian Academy of National Economy and Public Administration Graduate School of Corporate Management Moscow Russia A.A. Dorodnitsyna Frc Iu Ras Department of Economic Systems Mathematical Modeling Computing Center Moscow Russia

ISBN: (纸本)9781728110943

The article studies the social behavior of various age groups using experimental Economics methods. The conducted laboratory experiments show that the age of the participants and the specificity of the activity strongly influence the rate of infection spread. Simulation model with bots is constructed, the parameters of which can be adjusted to approximate the results obtained in experiments. © 2020 IEEE.

关键词： Economics

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A NONLINEAR LEAST-SQUARES CONVEXITY ENFORCING C⁰ INTERIOR PENALTY METHOD FOR THE MONGE–AMPÈRE EQUATION ON STRICTLY CONVEX SMOOTH PLANAR DOMAINS

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Communications of the American mathematical Society 2024年第14期4卷 607-640页

作者： Brenner, Susanne C. Sung, Li-Yeng Tan, Zhiyu Zhang, Hongchao Department of Mathematics and Center for Computation and Technology Louisiana State University Baton Rouge 70803 LA United States Center for Computation and Technology Louisiana State University Baton Rouge LA United States School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing Xiamen University Fujian 361005 China

We construct a nonlinear least-squares finite element method for computing the smooth convex solutions of the Dirichlet boundary value problem of the Monge-Ampère equation on strictly convex smooth domains in R². It is based on an isoparametric C⁰ finite element space with exotic degrees of freedom that can enforce the convexity of the approximate solutions. A priori and a posteriori error estimates together with corroborating numerical results are presented. © 2024 by the author(s) under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License (CC BY NC ND 4.0)

关键词： Monge-Ampère equation strictly convex smooth domains nonlinear least-squares convexity enforcing 𝐶⁰ interior penalty method enhanced cubic Lagrange finite elements isoparametric a priori and a posteriori error estimates active set algorithm

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Numerical investigation of light scattering by coupled plasmonic nanospheres using a high-accuracy multidomain Legendre pseudospectral time-domain method

Numerical investigation of light scattering by coupled plasm...

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2011 30th URSI General Assembly and scientific Symposium, URSIGASS 2011

作者： Chung, Shih-Yung Wang, Chih-Yu Teng, Chun-Hao Chen, Chung-Ping Chang, Hung-Chun Graduate Institute of Electronics Engineering National Taiwan University Taipei 10617 Taiwan Department of Applied Mathematics Center of Mathematical Modeling and Scientific Computing National Chiao Tung University Hsinchu 30010 Taiwan Graduate Institute of Electronics Engineering Department of Electrical Engineering National Taiwan University Taipei 10617 Taiwan Department of Electrical Engineering Graduate Institute of Photonics and Optoelectronics National Taiwan University Taipei 10617 Taiwan

ISBN: (纸本)9781424451173

A high-numerical-accuracy multidomain Legendre pseudospectral time-domain (PSTD) method is utilized to study the three-dimensional problem of light scattering by coupled metallic nanospheres and associated plasmonic resonances. With the multidomain technique, the simulation environment is partitioned into curvilinear hexahedral subdomains that well match the geometrical profile and material interfaces, which is an essential treatment to assure numerical accuracy, in particular, in near-field calculations. Cross sections are accurately calculated for studying the effects of different sphere radii and spacings. Interactions between two silver spheres are investigated for different incident wave propagation directions and polarizations. Electric near fields at plasmon resonances are examined. © 2011 IEEE.

关键词： Nanospheres

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