Two Graph Based Circuit Simulator for PDE-Electrical Analogy

The aim of the paper is to develop an efficient circuit simulator to solve circuits arising out of an electrical analogy for Partial Differential Equations (PDEs). This electrical analogy arises when we solve PDE through finite element method (FEM). The paper also proposes an optimal method for simulation of such circuits. We have built simulators based on Modified Nodal Analysis and Two Graph method for solution of PDEs through electrical analogy and compared their timing performance with commercial simulators. The timing performance of circuit simulators is improved for special PDE problems (such as Convection-diffusion) by an efficient implementation of iterative Cholesky with Two Graph method. The method is based on a graph representation of linear systems of equations. Such iterative methods would not be feasible with MNA. Using this method, we have been able to simulate circuits arising from the Convection-Diffusion problem with approximately 1.6 million nodes and 47 million edges in less than 8 minutes.