[1]刘其贵,吴金,肖志强,等.半导体器件模拟中求解线性系统的预条件处理方法[J].东南大学学报(自然科学版),2001,31(4):14-17.[doi:10.3969/j.issn.1001-0505.2001.04.004]
 Liu Qigui,Wu Jin,Xiao Zhiqiang,et al.Precondition Methods for Solving Linear Systems in Semiconductor Device Simulation[J].Journal of Southeast University (Natural Science Edition),2001,31(4):14-17.[doi:10.3969/j.issn.1001-0505.2001.04.004]
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半导体器件模拟中求解线性系统的预条件处理方法()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
31
期数:
2001年第4期
页码:
14-17
栏目:
电路与系统
出版日期:
2001-07-20

文章信息/Info

Title:
Precondition Methods for Solving Linear Systems in Semiconductor Device Simulation
作者:
刘其贵 吴金 肖志强 魏同立
东南大学微电子中心, 南京 210096
Author(s):
Liu Qigui Wu Jin Xiao Zhiqiang Wei Tongli
Microelectronic Center, Southeast University, Nanjing 210096, China)
关键词:
ILU ILUV ILUVP 预条件
Keywords:
ILU ILUV ILUVP pre-condition
分类号:
TN402
DOI:
10.3969/j.issn.1001-0505.2001.04.004
摘要:
对半导体器件模拟中求解线性方程组的预条件处理方法,即不完全LU分解方法进行了研究.首先介绍了ILU分解的理论基础,说明了采用预条件处理方法对解决线性方程组迭代求解收敛的重要性.然后介绍了由ILU方法发展而来的ILUV方法,并在对ILU和ILUV方法的理论研究和算法分析的基础上,提出了兼容以上2种方法优点的ILUVP方法,解决了ILUV方法中参数ψ的选取无法兼顾计算量和收敛速度不同要求的难题.最后通过对一个存在陡峭层分布的漂移扩散方程进行求解的实例,验证了算法的可行性和有效性.
Abstract:
This paper discusses the pre-condition methods (that is, the ILU methods) for solving the linear system in semiconductor device simulation.First, with the introduction to the theoretical foundation of ILU methods, the importance of applying pre-condition methods to solve the iterative convergence problem of linear equations is illustrated. Then, the ILUV methods, which were developed from the ILU methods are introduced. Based on the theoretical study and algorithmic analysis of those ILU and ILUV methods, the ILUVP method, which maintains the merits of those two methods and solves the problem that the selection of the parameter ψ in the ILUV method can not meet the different demands for both calculating amount and the convergence rate, is put forward. Finally, through an example of a drift-and-diffusion equation with steep distribution, the feasibility and effectivity of this algorithm are proved.

参考文献/References:

[1] 何野,魏同立.半导体器件的计算机模拟方法.北京:科学出版社,1979.24~40
[2] Sonneveld P.CGS—a fast Lanczos-type solver for nonsymmetric linear systems.SIAM J Sci Stat Comput,1979,10(1):36~52
[3] Polak S J.Semiconductor device modeling from the numerical point of view.Int J Numer Met Eng,1977,24:763~737
[4] Zhao Z Y,Zhang Q M,Tan G L,et al.A new preconditioner for CGS iteration in solving large sparse nonsymmetric linear equations in semiconductor device simulation.IEEE Trans on CAD,1991,10(11):1432~1440
[5] Ajiz M A,Jennings A.A robust incomplete Choleski-Conjugate gradient algorithm.Int J Numerical Methods in Engineering,1974,20:949~966
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备注/Memo

备注/Memo:
作者简介:刘其贵,男,1977年生,博士研究生.
基金项目:国家自然科学基金(69806002)和江苏省自然科学基金(BK97006)资助项目.
更新日期/Last Update: 2001-07-20