Improvement in norm-reducing Newton methods for circuit simulation

Abstract

The general convergence problems encountered when applying Newton's method to the circuit simulation domain are discussed. The authors identify and explore one source of difficulties for these methods and discuss a solution. The basic transconductance element, widely used to construct FET and bipolar transistor models, results in a pathological failure case for L/sub 2/-based norm-reducing methods due to the unidirectional nature between its input and output mode. Their particular solution retains the generic nature of norm-reducing methods but replaces the L/sub 2/-norm with a nonconsistent point of view. This norm determines which equations should converge first, prioritizes them, and guides the damping of the Newton updates accordingly. From a mathematical point of view, the steepest-descent direction in the Nu-norm is parallel to each Newton update at the iterate point and, therefore, allows more effective damping of the updates. The result has been an order-of-magnitude reduction in the number of Newton iterations. The performance of this norm on a series of high-electron-mobility transistor (HEMT) circuits is presented. The nonconsistency of the Nu-norm and its impact on global convergence properties for norm-reducing methods are discussed. >