| Foreword | 5 |
|---|
| Preface | 7 |
|---|
| Contents | 9 |
|---|
| List of Contributors | 14 |
|---|
| Parallel Transistor-Level Circuit Simulation | 17 |
|---|
| Introduction | 18 |
| Background | 18 |
| Parallelism Opportunities in Circuit Simulation | 20 |
| Parallel Netlist Parser | 20 |
| Parallel Approach for Nested Solver Loop | 21 |
| Device Evaluation | 22 |
| Linear Solvers for Circuit Simulation | 23 |
| Graph Mitigation using Multi-level Newton Methods | 27 |
| Multi-level Newton Method | 27 |
| Preserving Singleton Removal | 28 |
| Software | 29 |
| Parallel Linear Solver Strategy Comparison | 31 |
| Explanation of Tables | 31 |
| Numerical Results | 32 |
| Graph Mitigation Example | 34 |
| Conclusion | 35 |
| References | 36 |
| A Perspective on Fast-SPICE Simulation Technology | 38 |
|---|
| Introduction | 38 |
| SPICE: Transistor-Level Circuit Simulation | 39 |
| Usage and Limitations of SPICE | 41 |
| Need for Accelerated SPICE (`Fast-SPICE') Simulation | 42 |
| Fast-SPICE Technologies | 42 |
| SPICE vs. Fast-SPICE Techniques | 42 |
| Acceleration Technologies: Different Viewpoints | 45 |
| Examples of Fast-SPICE Technologies | 48 |
| Optimized Simulation of Parasitic Networks | 48 |
| Advanced Partitioning Technologies | 49 |
| Memory Simulation Acceleration | 50 |
| Challenges of Fast-SPICE and Future Research | 54 |
| References | 57 |
| Recent Advances in Structure-Preserving Model Order Reduction | 58 |
|---|
| Introduction | 58 |
| Description of RCL Networks | 60 |
| RCL Network Equations | 60 |
| RCL Transfer Functions | 63 |
| Passivity | 64 |
| Reciprocity | 64 |
| A Brief Review of Krylov Subspace-Based Model Order Reduction | 65 |
| Moment Matching and Padé Approximation | 65 |
| Reduced-Order Models | 67 |
| Moment Matching Via Krylov Subspace Methods | 68 |
| Passive Models Via Projection | 71 |
| Projection Combined with Krylov Subspaces | 71 |
| PRIMA | 72 |
| SPRIM | 73 |
| Preserving Block Structures | 73 |
| The Algorithm | 74 |
| Some Properties | 76 |
| Pros and Cons of PRIMA and SPRIM | 76 |
| Thick-Restart Krylov Subspace Techniques | 78 |
| Complex Expansion Points | 81 |
| Concluding Remarks | 83 |
| References | 84 |
| Injection Locking Analysis and Simulation of Weakly Coupled Oscillator Networks | 86 |
|---|
| Introduction | 86 |
| Oscillators | 88 |
| PPV/PRC Phase Macromodel of Single Oscillator | 89 |
| Malkin's Theorem | 90 |
| Injection Locking | 91 |
| Adler's Equation | 92 |
| Generalized Adler's Equation | 92 |
| Injection Locking Range of Ring Oscillator | 94 |
| Injection Locking Range of Hodgkin-Huxley Neuron | 96 |
| Coupled Oscillator Network Simulation | 98 |
| Coupled Oscillator Network Transient Simulation | 98 |
| Finding Oscillator Phases in the Synchronized State of a CON Numerically | 99 |
| PPV based Simulation of Ring Oscillator and Neuronal Oscillator Network | 102 |
| Conclusions | 107 |
| References | 107 |
| Dynamic Stability of Static Memories: Concepts and Advanced Numerical Analysis Techniques | 109 |
|---|
| Introduction | 109 |
| Static Noise Margins | 110 |
| Dynamic Stability Boundaries of Bistable Systems | 111 |
| Dynamic Noise Margins | 113 |
| Dynamic Read Noise Margin (DRNM) | 113 |
| Dynamic Write Noise Margin (DWNM) | 115 |
| Dynamic Hold Noise Margin (DHNM) | 116 |
| Relations to Conventional Static Noise Margins | 117 |
| Analysis of Dynamic Noise Margins | 117 |
| Computationally Efficient Tracing of Separatrices | 118 |
| Illustrative Examples | 120 |
| Numerical Stability of Separatrix Tracing | 123 |
| Extension to Memory Cells Modeled as High-Dimensional Systems | 125 |
| Conclusions | 126 |
| References | 127 |
| Recycling Circuit Simulation Techniques for
|