Specific problems of numerical analysis of the Josephson junction circuits
We describe solutions of two specific problems of numerical simulation of the Josephson junction circuits (these problems are not typical for the semiconductor electronics and thus had presumably not been considered in the designing of earlier CAD systems). The first one is modelling of circuits comprising many Josephson tunnel junctions within the framework of the microscopic ("Werthamer") theory resulting in nonlinear integro-differential relation between the junction current and voltage. Using a novel finite-difference scheme, an unexpected simple solution of this problem has been found. As a result, the computer time and memory necessary for the modelling are only three to five times larger than those for the similar analysis within the simplest RSJ model. The second problem is the optimum averaging of variables, necessary to filter out the Josephson and other high-frequency oscillations. We have solved this problem using ideas from the theory of digital time-dependent filters. The algorithms based on these methods are incorporated into our CAD program COMPASS which is extensively used for analysis of various analog and digital devices based on the Josephson effect.