## Efficient Simulation of Coupled Circuit-Field Problems: Generalized Falk Method

Citations: | 1 - 1 self |

### BibTeX

@MISC{Vu-quoc_efficientsimulation,

author = {Loc Vu-quoc and Yuhu Zhai and Khai D. T. Ngo and Senior Member},

title = {Efficient Simulation of Coupled Circuit-Field Problems: Generalized Falk Method},

year = {}

}

### OpenURL

### Abstract

Abstract—In this paper, we present an efficient method to solve the coupled circuit-field problem, by first transforming the partial differential equations (PDEs) governing the field problem into a simple one–dimensional (1-D) equivalent circuit system, which is then combined with the circuit part of the overall coupled problem. This transformation relies on the generalized Falk algorithm, which transforms the coordinates in any complex system of linear first-order ordinary differential equations (ODEs) or second-order undamped ODEs, resulting from the discretization of field PDEs, into guaranteed stable-and-passive 1-D equivalent circuit system. The generalized Falk algorithm, having a faster transformation time compared with the traditional Lanczos-type methods, transforms a general finite-element system represented by possibly a system of full matrices—capacitance and conductance matrices in heat problems, or mass and stiffness matrices in structural dynamics and electromagnetics—into an identity capacitance (mass) matrix and a tridiagonal conductance (stiffness) matrix. We also discuss issues related to the stability and the loss of orthogonality of the proposed algorithm. In circuit simulation, the generalized Falk algorithm does not produce unstable positive poles, and is thus more stable than the widely used Lanczos-type methods. The stability and passivity of the resulting 1-D equivalent circuit network are guaranteed since all transformed matrices remain positive definite. The resulting 1-D equivalent circuit system contains only resistors, capacitors, inductors, and current sources. The generalized Falk algorithm offers an extremely simple and convenient way to incorporate field problems into circuit simulators to efficiently solve coupled circuit-field problems. Numerical examples show a significant reduction of simulation time compared to the solution without using the proposed transformation.