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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.
Date of Publication: Nov. 2010