New Criteria Enhancing Robustness and Efficiency of Solving Systems of Circuit Equations

A new robust algorithm suppressing possible divergence of the Newton-Raphson method for solving the nonlinear circuit equations is proposed in both static and dynamic domains. For enhancing the efficiency of repeated solutions of linear systems necessary in the Newton-Raphson method, a new modification of the Markowitz criterion is suggested which is compatible with the fast modes of the LU factorization. The modified criterion consists in an estimation of probabilities of the fill-in enlargement. The probabilities are determined for all columns of the system matrix before the LU factorization, where the column probability is calculated as the average value of the probabilities for all the column elements. Finally, the columns are reordered so that first and last should be those with the minimum and maximum probabilities, respectively. As a verification of the proposed algorithm, a comprehensive set of numerical tests is described for circuits chosen from various parts of electronics