【作者】 王抒雁；

【导师】 胡继承； 王高峰；

【作者基本信息】 武汉大学 ， 计算数学， 2005， 硕士

【摘要】 随着大规模集成电路和电子计算机的迅速发展,电子电路的分析与设计方法发生了重大变革,传统的设计方法已远远不能满足要求,EDA技术已渗透到电子系统和专用集成电路设计的各个环节。在电路仿真软件SPICE(Simulation Program with lC Emphasis)中,对电路的模拟最后都转化为求解线性方程组Ax=6,其中A为对称的、非正定的、大型稀疏矩阵,在进行矩阵计算时采用的都是直接法(即LU分解法)。一般来说,直接法求解矩阵需要的运算次数是O(n~3),其中n为系数矩阵A的维数,并且在分解过程中会产生不少填充量,破坏矩阵的稀疏性,所以使用直接法需要较多的计算时间和存储空间。如果使用迭代法进行计算只需要O(n~2),但由于电路矩阵的特殊性,迭代法的选择需要考虑许多因素。 本文首先介绍了电路仿真的背景及相关概念,以及目前电路仿真软件中采用的矩阵计算方法,通过比较直接法与迭代法自然引出几种经典迭代法用于求解电路方程的结果,最后提出一种预处理方法与迭代法结合起来能有效的求解此类方程组,并将其分别与直接法、迭代法进行比较,得出此方法提高了运算效率的结论。更多还原

【Abstract】 With the development of large scales Integrated Circuit and electronic computers, the analysis and design methods of circuits have changed much. Traditional design methods can not meet new needs now. EDA technology has penetrated each step of the design of electronic systems and special Integrated Circuit. In SPICE (Simulation Program with Integrated Circuit Emphasis), the simulation of circuit is translated into solving linear equations Ax = b, where A is a symmetric, non-positive definite, large sparse matrix. The traditional method used to solve it is direct method (that is, LU factorization method). Generally speaking, the operation time of direct method is O(n~3), where n is the dimension of the coefficient matrix A, and during the process of factorization will generate many fill ins, so the sparsity of the matrix will be spoiled. If we use iterative method to solve the equations, the operation time needed is only O(n~2). So contrasted with iterative method, direct method needs more time and more memory. But because of the particularity of circuit matrices, the choice of iterative method need consider many factors.This paper introduced the background and relative concept of circuit simulation as well as the matrix computation method used in circuit simulation software now. Then through contrasting direct method and iterative method, gave the results of several iterative methods used in solving circuit matrix equations. The conclusion is that iterative method combined with a kind of preconditioning method can solve the equations efficiently and decrease the computation time.更多还原