An Essentially NonOscillatory ENO Adaptive Dynamic Table Model for Device Modeling

1
An Essentially Non-Oscillatory (ENO) Adaptive
Dynamic Table Model for Device Modeling

• Baolin Yang and Bruce McGaughy
• Cadence Design Systems, Inc.

2
Summary of Talk

• Table Model Basics
• Essentially Non-Oscillatory Approximation
• From 1D to Multidimensional
• Adaptive and Dynamic Table Model Building
• Numerical Results and Concluding Remarks

3
Table Model Basics

• I-V or Q-V curves approximated
• Interpolated values used in simulation
• Fast necessary for efficiency
• Smooth necessary for convergence
• Optimize accuracy, speed, and memory consumption

4
Drawbacks of Traditional Methods

• Linear table model used in some fast-spice
  simulators not accurate enough
• Not suitable for all applications
• Spline approximation expensive in evaluationand
  needs wider stencil for smoothing
• Averaged and mixed approximation expensivein
  evaluation
• No method systematic enough to achieve higher
  order smoothness

5
Comparison of Interpolation Methods
One-sided interpolation has oscillation!
6
ENO Approximation

• Essentially Non-Oscillatory (ENO)
  approximationis smooth
• Dynamic stencil
• v1, v2 , v3 for interpolation in v2, v3
• Criteria for stencil choosing based on
  aquantitative measurement of smoothness
• Newton divided difference
• Build the stencil systematically starting from 2
  points
• Good for any order

v1 v2 v3
v4
7
Advantages of ENO

• More compact stencil for smooth interpolation
• Dynamic stencil choosing systematic and easily
  extendible to higher order(4th order used in
  diode table model)
• Only uses polynomials in approximation
• Efficient to evaluate

8
Transfinite Blending

• Use transfinite blending function to blend ENO
  approximation in 1-D to multidimensional space
• Linear blending function used in practice
• For efficiency
• Number of cross terms less than straightforward
  tensor product approach
• Cross terms of the highest order basis function
  doesnt give much

9
Adaptive Error Control

• We control the error of ENO interpolation by
  adaptive local grid refinement
• When interpolation error is big in some
  region,we refine that region.
• With more than one levels of granularity, table
  model
• covers wider region and
• achieves more accuracy with limited memory

10
Dynamic Table Building

• Table model built on-the-fly
• Simulation enters some region -gt build the needed
  cells in that region
• Accuracy determines whether to build fine-gridor
  coarse-grid table

11
Numerical Results
Speed up 2x 5x
(CPU time in seconds)
12
Switched-Capacitor Filter
13
Fujitsu Memory Test
14
Comparing ENO and PWL Q-V
Bad enough! PWL I-V will
give us even more trouble!
15
Concluding Remarks

• ENO table model achieves accuracy and smoothness
  at the same time systematically
• Superior to all traditional methods
• Transfinite blending guarantees continuity and
  efficiency in evaluation
• Dynamic and adaptive table model building greatly
  reduces memory consumption
• Future work
• BJT table model