Homogénéisation d'un circuit électrique

Abstract

We derive the homogenized model of a periodic electric circuit including resistive devices, tension sources and current sources. The model derivation is based on a two-scale convergence which is based on the two-scale transform introduced by Arbogast, Douglas and Hornung (1990). The present two-scale convergence leads to the same results as the usual two-scale convergence introduced by Allaire. However, its statement is more general; in particular, it allows us to define easily the strong two-scale convergence, and it may be applied to functions defined on some periodical manifolds. Since electric circuits are considered as one-dimensional manifolds, the last point leads to the desired model.