Relaxation techniques for the simulation of VLSI circuits: by Jacob K. White and Alberto Sangiovanni-Vincentelli, from: Kluwer Academic Publishers, Norwell, MA, U.S.A.

Abstract

1 - Introduction.- Section 1.1 - Simulation For IC Design.- Section 1.2 - Circuit Simulation.- Section 1.3 - Standard Circuit Simulators.- Section 1.4 - Relaxation-Based Circuit Simulators.- Section 1.5 - Notation.- 2 - The Circuit Simulation Problem.- Section 2.1 - Formulation of the Equations.- Section2.1.1 - Branch Equations.- Section 2.1.2 - KCL and KVL.- Section 2.1.3 - Nodal Analysis.- Section 2.1.4 - Extending The Nodal Analysis Technique.- Section 2.2 - Mathematical Properties of the Equations.- Section 2.2.1 - Existence of Solutions.- Section 2.2.2 - Diagonal Dominance and the Capacitance Matrix.- Section 2.2.3 - Resistor-and-Grounded-Capacitor (RGC) Networks.- Section 2.3 - Numerical Integration Properties.- Section 2.3.1 - Consistency, Stability, and Convergence.- Section 2.3.2 - Stiffness and A-Stability.- Section 2.3.3 - Charge Conservation.- Section 2.3.4 - Domain of Dependence.- 3 - Numerical Techniques.- Section 3.1 - Numerical Integration in General-Purpose Simulators.- Section 3.2 - Properties of Multistep Integration Methods.- Section 3.3 - Relaxation Decomposition.- Section 3.4 - Semi-Implicit Numerical Integration Methods.- Section 3.5 - Relaxation Versus Semi-Implicit Integration.- 4 - Waveform Relaxation.- Section 4.1 - The Basic WR Algorithm.- Section 4.2 - Convergence Proof for the Basic WR Algorithm.- Section 4.3 - Waveform Relaxation-Newton Methods.- Section 4.4 - Nonstationary WR Algorithms.- 5 - Accelerating WR Convergence.- Section 5.1 - Uniformity of WR Convergence.- Section 5.2 - Partitioning Large Systems.- Section 5.3 - Ordering the Equations.- 6 - Discretized WR Algorithms.- Section 6.1 - The Global-Timestep Case.- Section 6.2 - Fixed Global-Timestep WR Convergence Theorem.- Section 6.3 - The Multirate WR Convergence Theorem.- 7 - The Implementation of WR.- Section 7.1 - Partitioning Mos Circuits.- Section 7.2 - Ordering the Subsystem Computation.- Section 7.3 - Computation of the Subsystem Waveforms.- Section 7.4 - Window Size Determination.- Section 7.5 - Partial Waveform Convergence.- Section 7.6 - Experimental Results.- 8 - Parallel WR Algorithms.- Section 8.1 - An Overview of the Shared-Memory Computer.- Section 8.2 - Mixed Seidel/Jacobi Parallel WR Algorithm.- Section 8.3 - Timepoint-Pipelining WR Algorithm.- Section 8.4 - Parallel Algorithm Test Results.- References.