Matrix Computation Methods In Circuit Simulation Software

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.