A Concept for Classification of Partial Differential Algebraic Equations in Nanoelectronics

Abstract

The design of electronic circuits is based on numerical simulation of corresponding mathematical models. Systems of differential algebraic equations (DAEs) reproduce the time behaviour of idealised electric networks. In nanoelectronics, miniaturisation causes parasitic effects, which can not be neglected any longer. These spatial phenomena yield models consisting of partial differential equations (PDEs). Thus the circuit's behaviour is given by partial differential algebraic equations (PDAEs), which couple DAEs in time and PDEs in time/space. We present a rough concept for classifying existing PDAE models in nanoelectronics. The categorisation rests primarily upon the physical background in each model.