Sparsing in Real Time Simulation

Modelling of mechatronical systems often leads to large DAEs with stiff components. In real time simulation neither implicit nor explicit methods can cope with such systems in an efficient way: explicit methods have to employ too small steps and implicit methods have to solve too large systems of equations. A solution of this general problem is to using a method that allows manipulations of the Jacobian by computing only those parts that are necessary for the stability of the method. Specifically, manipulation by sparsing aims at zeroing out certain elements of the Jacobian leading to a structure that can be exploited using sparse matrix techniques. The elements to be neglected are chosen by an a priori analysis phase that can be accomplished before the real-time simulation starts. In this article a sparsing criterion for the linearly implicit Euler method is derived that is based on block diagonalization and matrix perturbation theory.