Solution of PDEs-electrically coupled systems with electrical analogy

Abstract

This paper presents an approach to solve coupled systems where electrical/mechanical devices, whose behaviour is governed by a PDE or a system of PDEs, are connected together through an electrical circuit. In an earlier paper [1], it had been shown that PDEs can be modeled by an electrical equivalent circuit generated from the complete set of equations arising from the Finite Element Method (FEM). In this paper, the approach is extended to solve a system of PDEs. The approach allows the simulation of coupled systems with circuit simulation tools alone since the resultant system becomes an electrical circuit after an application of electrical analogy. The coupled system is solved by directly replacing PDE devices with the equivalent circuits. Further, a special circuit simulation technique, viz. multiport decomposition is used in order to solve a large coupled system. A sequential as well as a parallel simulator is built for coupled problems based on the proposed approach. A circuit with 100 linear PDE devices (the equivalent circuit contains 8 million nodes) has been simulated using the parallel simulator in less than 1h. We have achieved a speedup of 5 over the sequential simulator using 8 processors on distributed memory architecture. The characteristic of p–n junction diode (drift–diffusion equation) is analyzed by our circuit simulator to show that the proposed approach can be used to build a circuit-cum-device simulator.