Variational Methods for Solving Warped Multirate Partial Differential Algebraic Equations

Abstract

Signals exhibiting amplitude as well as frequency modulation at widely separated time scales arise in radio frequency (RF) applications. A multivariate model yields an adequate representation by decoupling the time scales of involved signals. Consequently, a system of differential algebraic equations (DAEs) modeling the electric circuit changes into a system of partial differential algebraic equations (PDAEs). The determination of an emerging local frequency function is crucial for the efficiency of this approach, since inappropriate choices produce many oscillations in the multivariate solution. Thus, the idea is to reduce oscillating behavior via minimizing the magnitude of partial derivatives. For this purpose, we apply variational calculus to obtain a necessary condition for a specific solution, which represents a minimum of an according functional. This condition can be included in numerical schemes computing the complete solution of the PDAE. Test results confirm that the used strategy ensures an efficient simulation of RF signals.