Complete LU decomposition conjugate residual method and its performance for large-scale circuit simulation

A method for solving large unsymmetric (LU) systems of linear equations arising from circuit transient analysis is proposed. This approach is based on the conjugate residual method, but is reinforced by the stability of LU decomposition. Unlike other preconditioned iterative methods, complete LU decomposition of a matrix at a previous time point is taken as a preconditioner of the current matrix to be solved. Only after the iterative process is judged to be nonconvergent is the current matrix decomposed. A novel test for the halt residual reduction is used to detect such a situation. Using this method, 10 LSI circuits with matrices ranging from 35 to 3668 equations have been analyzed. Correct transient solutions were obtained with only one to seven LU decompositions per hundred Newton-Raphson iterations and 8 to 40 iterations of conjugate residual on the average.<>