A Flexible Time-Stepping Scheme for Hybrid Field-Circuit Simulation Based on the Extended Time-Domain Finite Element Method

This paper describes a flexible time-stepping scheme for a recently developed hybrid field-circuit solver based on the extended time-domain finite element method (TDFEM) to alleviate the limitation on the use of a system-wide global time-step size. The proposed time-stepping scheme generalizes the strict synchronous coupling mechanism between the FEM and circuit subsystems and allows the signals in the different subsystems to be tracked and sampled at different time-step sizes. The signals from a slow subsystem with a larger time-step size are extrapolated, when necessary, for updating the signals in a fast subsystem with a smaller time-step size. The capability of the hybrid field-circuit solver with the proposed time-stepping scheme is further enhanced by the application of a tree-cotree splitting technique to the FEM subsystem, which helps reduce the iteration count per time step for a preconditioned iterative solution when the time-step size of the FEM subsystem becomes relatively large. With the flexibility of choosing subsystem-specific time-step sizes, the proposed time-stepping scheme improves the computational efficiency of the existing TDFEM-based hybrid field-circuit solver especially when the computational cost associated with the slow subsystems is much higher than that associated with the fast subsystems.

I. Introduction

The time-domain finite element method (TDFEM) has been demonstrated as a powerful and versatile simulation tool for analysis of a wide variety of electromagnetic devices including antenna arrays and microwave circuits [1], [2]. Recently, a hybrid field-circuit solver that combines the capabilities of the TDFEM and a SPICE-like circuit analysis was developed for accurate and efficient characterization of complicated microwave circuits that include both distributive and lumped-circuit components [3]. For simulations of even more complicated mixed-scale circuit systems that contain precharacterized blocks of discrete circuit elements, the hybrid field-circuit analysis implemented a systematic and efficient algorithm to incorporate multiport lumped networks in terms of frequency-dependent admittance matrices [4]. More recently, the TDFEM part of the hybrid field-circuit analysis was further enhanced by a tree-cotree splitting (TCS) technique [5], which enables the adoption of a larger time-step size (within the requirement of the temporal sampling rate) to speed up the time-marching process. The TCS technique also helps suppress the late-time linear drift or instability associated with the conventional TDFEM.