Iteration%20Technique%20toward%20SOC

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 todays 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

ILU Iteration Times Iteration Times ICD Iteration Times Iteration Times
residual Matrix I Matrix II residual Matrix I Matrix II
1e-3 165 5 1e-3 166 5
1e-6 258 8 1e-6 258 8
1e-10 377 11 1e-10 375 11
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

• Thats All
• Thank you!