One of our group member has successfully defended his Ph.D.. His thesis was on "Solution of Network Coupled Partial Differential Equations Through Electrical Analogy". Abstract of his thesis :
In the thesis, Partial Differential Equations (PDEs) are modeled by an electrical circuit generated from the equations arising from the Finite Element Method. This allows the solution of PDEs to be obtained through circuit simulation. One of the objectives of the thesis is to develop an efficient circuit simulator to solve circuits arising out of the electrical analogy for PDEs. For the simulation of such circuits, the thesis proposes efficient methods, describes their implementation and the results of experiments designed to evaluate their performance. Our electrical analogy naturally permits the simulation of coupled systems, where the electrical/mechanical devices whose behaviour is governed by PDEs are connected together through an electrical circuit. We have built sequential and parallel simulators for coupled problems based on the analogy and compared the performance of the simulators with standard coupled problem solvers. We have also designed and simulated the complete MEMS application using our simulators.
People usually solve electrical circuits using PDEs. Here, he converted system of PDEs to a electrical circuits and then solved them using BIT-SIM. BIT-SIM is a very fast circuit simulator (DC-Analyzer) developed here at IIT Bombay. BIT-SIM can handle circuits up-to few million nodes. It can but doesn’t support spice-models.
His work can be found here.