Using the LU Recombination Method to Extend the Application of Circuit-Oriented Finite Element Methods to Arbitrarily Low Frequencies

The circuit-oriented finite-element method (FEM) is a method that combines a finite-element field solver with a circuit analyzer and is suitable for analyzing electromagnetic field/circuit coupled problems. This paper describes a significant improvement to existing circuit-oriented FEMs that reduces the number of circuit elements and eliminates low-frequency stability problems. A modified LU recombination method is used to reformulate the original field-solver matrix equations. Circuits based on the reformulated equations are relatively insensitive to numerical errors and do not contain the small-value series resistors that circuit solvers are normally forced to add in order to guarantee a stable solution. Using this approach, the circuit-oriented FEM is capable of time-and/or frequency-domain simulations of problems containing linear or nonlinear lumped elements over a wide bandwidth. Examples are provided that demonstrate the ability of the new technique to model geometries from dc to several gigahertz in a single simulation.