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A stochastic galerkin method FOR MAXWELL EQUATIONS WITH UNCERTAINTY

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

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ON EFFECTIVE stochastic galerkin FINITE ELEMENT method FOR stochastic OPTIMAL CONTROL GOVERNED BY INTEGRAL-DIFFERENTIAL EQUATIONS WITH RANDOM COEFFICIENTS

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Journal of Computational Mathematics 2018年第2期36卷 183-201页

作者： Wanfang Shen Liang Ge School of Mathematic and Quantitative Economics Shandong University of Finance and Economics Jinan Shandong 250014 China School of Mathematical Sciences University of Jinan Jinan Shandong 250022 China

In this paper, we apply stochastic galerkin finite element methods to the optimal control problem governed by an elliptic integral-differential PDEs with random field. The control problem has the control constraints of obstacle type. A new gradient algorithm based on the pre-conditioner conjugate gradient algorithm （PCG） is developed for this optimal control problem. This algorithm can transform a part of the state equation matrix and co-state equation matrix into block diagonal matrix and then solve the optimal control systems iteratively. The proof of convergence for this algorithm is also discussed. Finally numerical examples of a medial size are presented to illustrate our theoretical results.

关键词： Effective gradient algorithm stochastic galerkin method Optimal controlproblem Elliptic integro-differential equations with random coefficients.

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Numerical comparison of three stochastic methods for nonlinear PN junction problems

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Frontiers of Mathematics in China 2014年第3期9卷 659-698页

作者： Wenqi YAO Tiao LU School of Mathematical Sciences Peking University Beijing 100871 China HEDPS CAPT and LMAM Peking University Beijing 100871 China

We apply the Monte Carlo, stochastic galerkin, and stochastic collocation methods to solving the drift-diffusion equations coupled with the Poisson equation arising in semiconductor devices with random rough surfaces. Instead of dividing the rough surface into slices, we use stochastic mapping to transform the original deterministic equations in a random domain into stochastic equations in the corresponding deterministic domain. A finite element discretization with the help of AFEPack is applied to the physical space, and the equations obtained are solved by the approximate Newton iterative method. Comparison of the three stochastic methods through numerical experiment on different PN junctions are given. The numerical results show that, for such a complicated nonlinear problem, the stochastic galerkin method has no obvious advantages on efficiency except accuracy over the other two methods, and the stochastic collocation method combines the accuracy of the stochastic galerkin method and the easy implementation of the Monte Carlo method.

关键词： stochastic partial differential equation stochastic galerkin method stochastic collocation method Monte Carlo method

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Nonlinear stochastic galerkin and Collocation methods:Application to a Ferromagnetic Cylinder Rotating at High Speed

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Communications in Computational Physics 2010年第10期8卷 947-975页

作者： Eveline Rosseel Herbert De Gersem Stefan Vandewalle Computer Science Department K.U.LeuvenCelestijnenlaan 200A3001 LeuvenBelgium Faculty of Sciences K.U.LeuvenEtienne Sabbelaan 538500 KortrijkBelgium

The stochastic galerkin and stochastic collocation method are two state-ofthe-art methods for solving partial differential equations(PDE)containing random *** the latter method,which is based on sampling,can straightforwardly be applied to nonlinear stochastic PDEs,this is nontrivial for the stochastic galerkin method and approximations are *** this paper,both methods are used for constructing high-order solutions of a nonlinear stochastic PDE representing the magnetic vector potential in a ferromagnetic rotating *** model can be used for designing solid-rotor induction machines in various machining tools.A precise design requires to take ferromagnetic saturation effects into account and uncertainty on the nonlinear magnetic material *** issues of the stochastic galerkin method are addressed and a numerical comparison of the computational cost and accuracy of both methods is *** stochastic galerkin method requires in general less stochastic unknowns than the stochastic collocation approach to reach a certain level of accuracy,however at a higher computational cost.

关键词： Nonlinear PDE with random coefficients polynomial chaos stochastic collocation method stochastic galerkin method electromagnetics

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stochastic Analysis of Interconnect Delay in the Presence of Process Variations

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Journal of Semiconductors 2008年第2期29卷 304-309页

作者：李鑫 Janet M.Wang 唐卫清吴慧中南京理工大学计算机科学与技术学院南京210094 亚利桑那大学电子工程系中国科学院计算技术研究所北京100080

Process variations can reduce the accuracy in estimation of interconnect performance. This work presents a process variation based stochastic model and proposes an effective analytical method to estimate interconnect delay. The technique decouples the stochastic interconnect segments by an improved decoupling method. Combined with a polynomial chaos expression （PCE）, this paper applies the stochastic galerkin method （SGM） to analyze the system response. A finite representation of interconnect delay is then obtained with the complex approximation method and the bisection method. Results from the analysis match well with those from SPICE. Moreover, the method shows good computational efficiency, as the running time is much less than the SPICE simulation＇s.

关键词： coupled interconnects process variations stochastic modeling delay estimation stochastic galerkin method polynomial chaos expression

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