Applications of Multilinear and Waveform Relaxation Methods for Efficient Simulation of Interconnect-Dominated Nonlinear Networks

Abstract

Applications of multilinear and waveform relaxation methods are presented for efficient transient analysis of interconnect-dominated nonlinear networks. In this paper, two procedures that realize these well-known and fundamental theories in conventional circuit simulation tools are developed by taking advantage of the unique characteristics of interconnect networks. The multilinear theory uses the Volterra functional series to decompose the nonlinear network into multiple linear networks. Then, the solutions of the mildly nonlinear network are obtained from the linear combinations of sequences of responses of the decomposed linear networks. On the other hand, the waveform relaxation technique is used to solve networks with strong nonlinearity. The networks are partitioned into linear and nonlinear subnetworks and each subnetwork is solved iteratively using the waveform relaxation technique. Simplified analysis steps that give good insight into these techniques are also derived analytically. Finally, the accuracy and efficiency of the methods are verified with two examples.

A two-level waveform relaxation approach for fast transient simulation of long high-speed interconnects

“…This paper addresses the problem of efficient circuitbased transient simulation of high-performance chip-to-chip links [1], [2]. Such structures pose several challenges.…”

“…Standard FFT methods may be used to recover the timedomain impulse or step responses, which in turn may be processed to derive global metrics such as eye diagram openings or Bit Error Rate (BER) statistics [1]- [4]. The main drawback of this approach is the intrinsic assumption of linearity.…”

Optimized waveform relaxation solution of RLCG transmission line type circuits

“…Since then the WR algorithms have evolved to the solution of circuits and PDEs in parallel. The WR approach was applied to a multitude of problems in the circuit theory area, see for example [4]- [6], and in the partial differential equations of evolution type area, see for example [7]- [9] and references therein. In all of the WR techniques, the processors exchange appropriate waveforms between subsystems or subcircuits, and the natural coupling between blocks of components of the circuit (system) is preserved by so-called transmission conditions.…”

Longitudinal partitioning based waveform relaxation algorithm for transient analysis of long delay transmission lines

“…Presently, various approaches exist for applying the waveform relaxation to transmission line networks [3]- [6]. In [3], the waveform relaxation was applied to the generalized method of characteristics (MoC) which partitioned the line into two weakly coupled subcircuits.…”

“…Hence, efficient waveform relaxation algorithms for simulation of long delay transmission lines based on longitudinal partitioning of the line is still an open problem. Other waveform relaxation algorithms are based on partitioning the linear transmission line network from the nonlinear terminations [6].…”