Relaxation Techniques for the Simulation of VLSI Circuits / Edition 1

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Table of Contents

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.

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