Efficient simulation of coupled circuit-field problems: generalized Falk method

The proposed generalized Falk (GF) method offers an extremely simple and convenient way to solve coupled circuit-field problems in circuit simulators by transforming the discretized governing-field equations into guaranteed stable-and-passive one-dimensional (1D) equivalent-circuit systems, which are then combined with the circuit part of the overall coupled problem. More efficient than the traditional Lanczos-type methods, the GF method transforms a general finite-element system represented by a system of full matrices into an identity capacitance (mass) matrix and a tridiagonal conductance (stiffness) matrix. No positive poles are produced; all transformed matrices remain positive definite. The resulting 1D equivalent-circuit system contains only resistors, capacitors, inductors, and current sources. Several numerical examples are provided.