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 ILUIteration TimesICDIteration Times residualMatrix IMatrix IIresidualMatrix IMatrix II 1e-316551e-31665 1e-625881e-62588 1e-10377111e-1037511

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 ！