Solving nonlinear resistive networks using piecewise-linear analysis and simplicial subdivision

In recent years numerous results of piecewise-linear analysis of nonlinear resistive networks have been derived. The applicability of the method relies on the fact that every nonlinear device is modeled by a piecewise-linear continuous function. In order to extend the applicability of piecewise-linear analysis to treat more general nonlinear networks, three steps need to be carried out: i) the subdivision of the domain of the multi-dimensional nonlinear network function; ii) the interpolation of a piecewise-linear continuous function on the subdivided domain; and iii) the application of piecewise-linear analysis. It turns out that the above three steps can be accomplished effectively by using simplicial subdivision. In addition, the difficulties encountered in the conventional piecewise-linear analysis are simplified. The memory space needed for the analysis is also greatly reduced. The complete analysis has been implemented in a program on CDC 6400.