Accelerated waveform methods for parallel transient simulation of semiconductor devices

This paper presents an optimized Waveform Relaxation solver for electrically-long high-speed channels terminated by nonlinear networks. The time-domain scattering operators of channel and terminations are cast as recursive convolutions and nonlinear discrete-time filters, respectively. A transverse and longitudinal decoupling is then applied to the channel operator, with the introduction of suitable relaxation sources, and solved iteratively until convergence. A frequency-dependent over-relaxation parameter is introduced in order to optimize the convergence rate. Numerical results show significantly reduced runtime and iteration count for critical benchmarks with respect to previous Waveform Relaxation formulations.

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“…over the set of poles , residues , and direct coupling constant ∞ in (12). We remark that if = 0 a standard Vector Fitting scheme is obtained.…”

Section: B Suboptimal Rational Over-relaxationmentioning

confidence: 95%

Fast iterative simulation of high-speed channels via frequency-dependent over-relaxation

Chinea

Grivet-Talocia

et al. 2011

2011 IEEE 20th Conference on Electrical Performance of Electronic Packaging and Systems

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“…Using now the initial conditions (43) and the definition of the outer relaxation sources (44), we obtain the expression…”

Section: A Convergence Analysismentioning

confidence: 99%

Transient Simulation of Complex High-Speed Channels via Waveform Relaxation

Loggia

Grivet-Talocia

2011

IEEE Trans. Compon., Packag. Manufact. Technol.

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“…These accelerating techniques include windowing, Krylov subspace methods, matrix splitting etc. (see [7,9,10,12,14,16]). These techniques, of which the simplest one is windowing, can speed up convergence behaviors of WR.…”

Section: Introductionmentioning

confidence: 99%