Solving the Linear Complementarity Problem in Circuit Simulation

Abstract

In the simulation of electronic circuits piecewise linear modelling yields a global circuit description which in principle can be used to solve for a circuit response in a finite number of steps. During the solution process a sequence of linear complementarily problems (LCP) has to be solved within the piecewise linear system description. The purpose of this paper is to present and discuss some new methods to solve this LCP for certain matrix classes. To start with, two types of LCP solution algorithms are briefly described: pivoting algorithms and the modulus algorithm. It is shown that these algorithms have certain disadvantages if applied to the problem as stated above. Those problems can be overcome by the new methods to be presented. The first one is a modified version of an iterative algorithm of 0. L. Mangasarian. The second one is a so-called simplicial method, based on a new integer labelling and an efficient labelling algorithm. Convergence conditions are given, as is a bound for the error in the approximate solution. In both new algorithms full advantage can be taken of sparse matrix techniques. The labelling algorithm turns out to converge for a large class of matrices, comparable with standard pivoting methods.