Iteration Technique toward SOC

1. Iteration Technique toward SOC EDA Lab, Department of Computer Science and Technology, Tsinghua University 2005.8

2. Outline • Part One • Simulation vs. Iteration • Problem Size in the Future • Future Trend of Simulation • Part Two • P/G Simulation • More Accurate Model • Numerical Character • Accelerate Convergency Speed • Universal Formulation

3. Simulation vs. Iteration • Linear System • Large Scale Differential Equations • Topology of Differential Variable • Numerical method need Iteration • Non-Linear System • Successful Commercial Simulator • Spice/HSpice/PSpice • ADS（Agilent Design System）

4. Problem Size in the Future • More Than Two Billion Transistors • More Metal Layers • Complicated Interconnect Techniques • Local Simulation Size is equal to today’s Global Simulation Size

5. Future Trend of Simulation • More Accurate Simulation Model • More Efficient Local Simulator • Utilize the Geometry Similarity • Accelearte Iteration Convergency Speed • Reuse of Iteration Result • Model Reduction in Analytical Form • Parallel Global Simulation • SMP • Cluster

6. P/G Simulation • Different Topology • Physical Factors to be Considered • Static and Dynamic Simulation Technique • Design and Optimization Technique

7. More Accurate Model • Consider Package

8. More Accurate Model • Consider Vias

9. Numerical Character • Matrix Stamp Order

10. Numerical Character • Matrix Shape

11. Numerical Character • Poorer Eigenvalue

12. Numerical Character • Iteration Times Comparision

13. Accelerate Convergency Speed • Balance Technique

14. Accelerate Convergency Speed • Result

15. Universal Formulation • Famouse NA Formulation in P/G Simulation • Universal MNA Formualtion in General Simulation • Gap Here is Numerical Problem • Improve Preconditioner to Break the Gap

16. Universal Formulation • Simple Preconditioner Fit MNA • More Efficient One

17. Conclusion • Pay more attention to topolgy and geometry • Trying to find out analytical result instead of using iteration • When considering an algorithm, think about whether it is easy to be implement in parallel form • Construct as many reusable data as possible

18. That’s All Thank you！