An intelligent partial Gauss-Seidel scheme (PGS) for general circuit simulation is described. This approach is a novel combination of direct solution using incomplete LU factorization, and iterative solution using Gauss-Seidel relaxation. The method converges faster and more reliably than Gauss-Seidel, while taking a comparable amount of execution time per iteration. Reliable analytic rules are derived such that terms that would be relaxed in Gauss-Seidel are relaxed only if they are considered small by applying these rules. Solution speeds up to ten times faster than direct methods have been demonstrated and higher gains are anticipated for larger circuits. This scheme is robust and accurate for circuits with many different element types, including bipolar transistors, MOSFETs, diodes, inductors, and dependent sources.>

The improvement in computational throughput of VLSI circuit simulation is addressed. A high degree of natural parallelism exists in the circuit simulation problem; potentially a large number of processor can be used efficiently. Three distinct approaches for obtaining parallel execution in direct-method circuit simulators are investigated. These approaches differ primarily in the size of the individual tasks used to obtain parallel execution. The relative advantages of each approach are examined, and performance data from simulations on parallel processing systems are presented. For the third approach, very good parallel efficiency was obtained; in some cases, 99% parallelism has been observed.>

The authors present a general purpose, parallel matrix solver based on the conjugate gradient squared (CGS) method which features a novel preconditioning scheme commensurate with massive parallel computing. The solver algorithm has been successfully used for solving linear systems of equations arising from circuit and device simulations with MOS and bipolar junction transistor (BJT) circuits, both digital and analog, as well as high-level injection conditions in devices. The performance of the algorithm can be further improved by a matrix partitioning scheme.>

Two techniques for general circuit simulation, an intelligent, partial Gauss-Seidel scheme (PGS) and a preconditioned conjugate-gradient scheme (PLUCGS), are described. Both techniques are robust and accurate for bipolar and MOS analog and digital circuits. PGS is a novel combination of direct solution, using LU factorization, and iterative solution, using Gauss-Seidel relaxation. The method converges faster and more reliably than Gauss-Seidel, while taking a comparable amount of execution time per iteration. Solution speeds up to 6 times faster than direct methods have been demonstrated and higher grains are anticipated for larger circuits. The second method, PLUCGS, uses a partial LU factorization as a preconditioner; a vectorized implementation on a CONVEX C-240 computer is 5-7 times faster than the direct solution method with only one-fourth the memory requirements.>

To exploit time-domain latency in circuit simulation using direct methods, an accurate, computationally efficient model for slowly moving, dormant portions of the circuit is required. A new, implicit integration method, the overdetermined polynomial method (ODPM), has been developed which permits the formulation of an accurate latent model. Using the ODPM integration method, the Jacobian of a dormant subcircuit need not be reevaluated over a large number of time steps of varying size. An accurate Norton equivalent circuit that emulates the impedance and current characteristics of the subcircuit can be obtained without reevaluation of the Jacobian or nonlinear charge computations. This new approach for utilizing latency produces significant improvements in circuit simulation speed with no decrease in accuracy or generality. The authors have demonstrated speed gains of 3 to 20 times over TISPICE for several large circuits.>

An approach for modeling dormant subcircuits is presented that utilizes iteration latency to provide speed improvements that are comparable to the potential speed improvements of an independent time step approach. This scheme minimizes the work required on the first iteration at a time point, which is the normal limiting factor in iteration latency schemes. However, since simulations are performed for each subcircuit at each time point, the penalty for backing up when truncation error is unacceptable is minimized.>

Two techniques are presented for optimizing the parametric yield of digital MOS circuit blocks for VLSI designs. The first is based on quasi-Newton methods and utilizes the gradient of the yield. A novel technique for computing this yield gradient is derived and algorithms for its implementation are discussed. Geometrical considerations motivate the second method which formulates the problem in terms of a minimax problem. Both yield optimization techniques utilize transient sensitivity information from circuit simulations. Encouraging results have been obtained thus far; several circuit examples are included to demonstrate these techniques.>

An integrated and efficient approach is developed for automated statistical circuit design. One major problem in statistical circuit design for MOS VLSI is the prohibitively expensive computational requirements. The objective is to find realistic, accurate, and efficient solutions for use in the MOS VLSI design area. An automated statistical characterization system has been developed to characterize a large number of MOS devices to obtain statistical information on device parameters. A statistical model for MOS VLSI circuits has been developed in which only the interdie variations are considered, since they are much larger than the local intradie variations. Therefore, the set of statistical variables are different from the set of design parameters, and this leads to a resolution of the problem of dimensionality associated with statistical design. In this statistical model, variations in device length and width, oxide capacitance, and flat band voltage, have been shown to be the principal process factors responsible for the statistical variation of device characteristics. A scalable MOS model has been developed to represent changes in the device model parameters as functions of these principal factors. This accurate and simple statistical modeling approach uses only four statistical variables, and thus permits computationally efficient statistical parametric yield estimation (SPYE). The direct approach for transient sensitivity computation has been implemented in SPICE to allow very efficient computation of performance function sensitivities. An efficient technique for computing the yield gradient using the SPYE and transient sensitivity results is discussed and an example is presented to demonstrate its use in parametric yield optimization.