Titlebook: Relaxation Techniques for the Simulation of VLSI Circuits; Jacob K. White,Alberto Sangiovanni-Vincentelli Book 1987 Kluwer Academic Publis

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Introduction,ptability. In fact, a breadboard may give results which have little resemblance to the manufactured circuit performances due to their completely different parasitic components. Simulation programs are also used to avoid the fabrication of prototype integrated circuits because fabrication and testing

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Numerical Techniques,ntial equation systems generated from circuit descriptions, the method must have several strong properties. For this reason, general purpose circuit simulation programs, like SPICE2[2] and ASTAP[3], use very robust numerical integration algorithms, members of the class of .. In the first section of

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Waveform Relaxation,anging at very different rates. This is because the direct application of the integration method forces every differential equation in the system to be discretized identically, and this discretization must be fine enough so that the fastest-changing state variable in the system is accurately represe

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Accelerating WR Convergence,be described. In this chapter the theoretical background for three of these techniques will be presented. We will first analyze nonuniformity in WR convergence, which explains why breaking the simulation interval into pieces, called windows, can be used to reduce the number of relaxation iterations

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Discretized WR Algorithms,istep integration formulas are used to solve for the iteration waveforms, the differential equations that describe the decomposed systems will not be solved exactly. Therefore, the convergence theorem presented in Section 4.2 does not guarantee the convergence of this . WR algorithm. However, the di

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Introduction, of an integrated circuit to verify a design is both expensive and time-consuming. Moreover, extensive probing is not possible and modification of circuit components to determine a better design is practically infeasible.