Anyone who has ever approached VLSI design may have sensed the importance of using a good circuit simulator that can save his or her company large sums of money if it can provide an accurate analysis of IC performance. This book outlines the highly advanced topics of circuit simulation with respect to the time-domain transient analysis that appears to be most expensive in terms of computer time.
It is the first book to present the description of the entire circuit simulation process, with particular emphasis on relaxation algorithms for solving circuit differential equations. The relaxation approach has become the preferred technique for MOS VLSI circuits because they are unidirectional.
The book consists of eight chapters:
(1) Introduction--contains a brief review of IC simulation levels, existing simulation techniques, and available packages.
(2) The Circuit Simulation Problem--presents the formulation of the equations, the mathematical properties of the equations, and the numerical integration properties.
(3) Numerical Techniques--examines numerical integration in general purpose simulators, the properties of multistep integration methods, and the relaxation and semi-implicit integration methods, which are compared to each other on the basis of their dependence domains.
(4) Waveform Relaxation--gives the basic WR algorithm and the proof of its convergence; it also describes waveform relaxation-Newton methods and non-stationary WR algorithms.
(5) Accelerating WR Convergence--shows the theoretical background of three techniques to improve the efficiency and robustness of the WR algorithm, namely, windowing the simulation interval, partitioning large systems, and ordering the equations.
(6) Discretized WR Algorithms--investigates the effects of using the global-timestep and the multirate-timestep cases.
(7) The Implementation of WR--describes how the RELAX2 program performs crucial simulation steps: partitioning MOS circuits, ordering the subsystem computation and the computation of subsystem waveforms that exploit the benefits of incorporating window size determination and partial waveform convergence. Experimental results give impressive figures supporting WR simulation techniques over their direct simulation counterparts for a wide range of MOS circuits.
(8) Parallel WR Algorithms--exhibits the most exciting prospects of the implementation strategy, that is, using distributed shared-memory (with caches) architectures and specially organized parallel algorithms (combined Gauss-Seidel and Gauss-Jacobi relaxation and piped waveform computation).
The book’s declared goals are not as ambitious as they might have been; they have apparently been fulfilled. The primary goal is to present the mass of mathematical and experimental results (developed over the past 20 years by a large body of academics and students whose efforts are appropriately cited in the well-balanced list of 81 references) on the application of the relaxation techniques to circuit simulation. The presentation is mathematically rigorous and relevant; at the same time, it preserves the natural intuitive simplicity of the simulation idea. This goal has been achieved by beginning each section of the text with either an informal problem formulation or a simple MOS circuit example and by ending it with a clear interpretation of the theorems, observations, and algorithms displayed in between. This kind of presentation allows the reader to skim the text rapidly and efficiently in order to capture the basic ideas. All examples provided effectively test the reader’s understanding and imagination. For a detailed reading of the text, some knowledge of linear algebra and functional analysis is recommended. Another goal of the book is to act as a guide to the computational and implementational issues in the development of the relaxation-based circuit simulators. This goal is met through a comprehensive and omnipresent comparative assessment of methods, algorithms, and simulator performance with respect to various properties and criteria. My only complaint is that the comparative data are not tabulated in a cumulative appendix. However, this would make the book more of a reference volume.
Although the book is not a textbook, its topical and organizational uniqueness would make it an excellent tutorial for electrical and electronic engineering students in VLSI simulation courses. It would also be good for computer science postgraduates seeking new ideas on parallel architectures for simulation and applied mathematics postgraduates seeking new ideas on numerical analysis applications.
