Improvement in norm-reducing Newton methods for circuit simulation

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 L₂-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 L₂-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