Iteration Dependent Waveform Relaxation for Hybrid Field Nonlinear Circuit Problems

A Waveform Relaxation Solver for Transient Simulation of Large-Scale Nonlinearly Loaded Shielding Structures

“…With respect to [25], a time-partitioning strategy [18] is embedded in the solver formulation to improve the convergence property of the WR-NGMRES scheme and to handle the large number of ports of the presented application. A different approach, still within the adopted decoupling and WR framework, was introduced in [14]. Nevertheless, the presented solver significantly differs from [14] for several reasons.…”

“…A different approach, still within the adopted decoupling and WR framework, was introduced in [14]. Nevertheless, the presented solver significantly differs from [14] for several reasons.…”

“…1) The basic WR scheme was modified in [14] with an iteration-dependent strategy that changes the macromodel reference impedance (i.e., R0) to match a time-varying impedance level at the decoupling ports. This choice requires the generation of a possibly large number of scattering macromodels referenced to different port impedances, increasing the runtime requirements of the preprocessing phase, whereas the proposed approach is based on a single (compressed) macromodel and does not include any iteration-dependent parameter.…”

“…2) The proposed approach takes advantage of the WR-based iteration of the WR-NGMRES scheme [25], while Wendt et al [14] solve for the basic WR-LP iteration.…”

“…Removing such components leaves an unloaded enclosure whose behavior is governed by linear Maxwell's equations, and which can be characterized both in time and frequency domain. This consideration enables hybrid simulation approaches [13], [14] based on partitioning the system into the linear electromagnetic (yellow box and dark strips in Fig. 1) and nonlinear (red blocks) subdomains, which are characterized separately.…”