CLUCGS and CLUCR - two matrix solution methods for general circuit simulation

Direct methods and iterative methods have been used in most analog circuit analysis tools for matrix solution. But neither can efficiently solve the large-scale sparse matrix or ill matrix because of the closely coupled relationship of execution time and matrix size for direct methods and the convergence problem for iterative methods. This paper presents two methods that are a combination of direct solution using complete LU factorization and iterative solution using conjugate gradient square (CGS) or conjugate residual (CR) method. The methods converge faster and more reliably than the LU factorization method and conjugate gradient (CG) method, and can achieve high resolution on a wide variety of circuits. A very efficient preconditioning method is used in our approach to accelerate convergence. Furthermore, we present an effective judgment method for re-factorization of matrix. Several numerical experiments results are included to compare their efficiencies.