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

Hu, Haisheng; Chinea, A.; Grivet-Talocia, S.; Miscuglio, Mario

doi:10.1109/epeps.2011.6100202

Cited by 2 publications

(3 citation statements)

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“…Convergence holds only if P is a contraction, as discussed in [30], [36], and [49]. This condition is not always verified [50], [51], and more robust approaches are required.…”

Section: Wr Approachesmentioning

confidence: 92%

“…We use here the same channels already introduced in [29], consisting of intranode, internode, or node-to-peripheral electrical interconnects in highend server systems. More details on these structures, as well as a complete documentation of the corresponding delayrational macromodels, are available in [29] and [51]. Under the electrical modeling standpoint, each channel consists of Q = 9 single-ended coupled links, resulting in P = 18 electrical interface ports.…”

Section: A Channelsmentioning

confidence: 99%

“…Unfortunately, the analysis in [49] shows that when transverse partitioning (TP) is introduced to improve simulation efficiency, the convergence of the WR scheme is only conditional and cannot be guaranteed in all cases, despite some improvements based on possibly frequency-dependent over-relaxation have been documented [50], [51]. This consideration motivated the approach in [52] and [53], where more robust iterative solvers have been suggested to replace the fixed point iteration typical of basic WR implementations.…”

mentioning

confidence: 96%

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Macromodel-Based Iterative Solvers for Simulation of High-Speed Links With Nonlinear Terminations

Olivadese

Grivet-Talocia

Siviero

et al. 2014

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

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Data transmission on high-speed channels may be affected by several undesired effects, including coupling from nearby interconnects, dispersion, losses, signal reflections from terminations and from internal discontinuities, and nonlinear/dynamic effects of drivers and receivers. The latter are often neglected, leading to very fast solvers, whose results may, however, be questionable when driver/receiver nonlinearities are important. This paper presents a framework for the transient analysis of complex high-speed channels with arbitrary nonlinear termination circuits. The approach is based on decoupling channel and terminations through a scattering-based waveform relaxation (WR) formulation. The channels are here cast as delay-rational macromodels, which are solved in discrete time domain through fast delayed recursive convolutions. The terminations can be either arbitrary circuits, solved by SPICE, or nonlinear behavioral macromodels, which are here formulated in discrete-time scattering representations. To overcome the known convergence issues of standard WR methods, we apply here more general iterative solution schemes, such as generalized minimal residual and biconjugate gradient stabilized, integrated into inexact Newton iterations, obtaining a set of numerical schemes with guaranteed convergence. The excellent performance of the proposed approach is illustrated on a large set of benchmarks.

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“…Convergence holds only if P is a contraction, as discussed in [30], [36], and [49]. This condition is not always verified [50], [51], and more robust approaches are required.…”

Section: Wr Approachesmentioning

confidence: 92%