Simulation of large-scale periodic circuits by a homogenization method

Actuation, sensoring and control in arrays of MEMS require spatially distributed periodic electronic circuits. For very large sized arrays, say 1000 times 1000 MEMS or cells, on the same chip, simulation requirements for electronics are far away from standard algorithm capabilities. One of the authors has shown in a theoretical paper, that a homogenization modeling method, previously developed for composite materials, can be extended to arrays of electronic circuits, at least in the linear static case. When it is applied to a set of periodic network equations, the simplified resulting model turns to be a system of few partial differential equations. Its properties are inherited on the one hand from the periodic cell composition, and on the other hand from electric conditions imposed at the boundaries. Its numerical solution, a vector of few mean voltages, is weakly dependent of the array size. Actual voltages, at all nodes of the whole periodic circuit, are computed through a fast post-processing procedure. We present the implementation of the model.