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

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

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 ）

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

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

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

More Accurate Model Consider Package

More Accurate Model Consider Vias

Numerical Character Matrix Stamp Order

Numerical Character Matrix Shape

Numerical Character Poorer Eigenvalue

Numerical Character Iteration Times Comparision ILUIteration TimesICDIteration Times residualMatrix IMatrix IIresidualMatrix IMatrix II 1e e e e e e

Accelerate Convergency Speed Balance Technique

Accelerate Convergency Speed Result

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

Universal Formulation Simple Preconditioner Fit MNA More Efficient One

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

That’s All Thank you ！