SMBinterp: an N-th-Order Accurate, Distributed Interpolation Library

Motivation

Pratt & Whitney

Pratt and Whitney logo

Pratt & Whitney: a History

Pratt and Whitney logo

Pratt & Whitney: a History

Pratt and Whitney logo

CFD Interfaces

CFD Interfaces

Multiphysics Simulation

Pratt and Whitney 4000 Engine Simulation

Mesh Element Disparity

Pratt and Whitney 4000 Engine Simulation

State of Multiphysics Interpolation

Multiphysics Applications

Pratt and Whitney 4000 Engine Simulation

Two Problems

  1. Time-Efficient Data Lookup
  2. Accurate Interpolation

CHIMPS

CHIMPS

CHIMPS overview

CHIMPS

Geometry used for 2D Baker Method

CHIMPS

Tri-Linear Interpolation

AVUSINTERP

AVUSINTERP

Baker's Method Geometry

AVUSINTERP

Baker's Method

AVUSINTERP

What did I do?

What did I do?

Python Logo

SMBinterp

CHIMPS   U   AVUSINTERP

Baker's Method Distribution Architecture

Baker's Method

Baker's Method

Geometry used for 2D Baker Method

Baker's Method

Geometry used for 2D Baker Method

Baker's Method

Baker 1

Higher Orders and Dimensions

Baker: Linear 2D

Baker 5

Baker: Linear 3D

Baker 5

Baker: Error 2D, Quadratic

Baker 2D Quadratic Error Equation

Baker: Error 2D, Cubic

Baker 2D Cubic Error Equation

Pattern

Baker 3D Quadratic Error Equation

Memoization

Baker 3D Quadratic Error Equation

Interpolation Scheme Results

Gmsh Resolution 1

Gmsh 1

Gmsh Resolution 2

Gmsh 2

Exact Function:

Exact Equation Plot of Exact Equation

Root Mean Square

RMS Equation

Total RMS Error

Results of Mesh Resolution Study

Parameter Tweaking

Results of Parametric Study

Truthiness

Results of Parametric Study

Timing

Timing Results

Timing

Timing Results

Distribution Scheme

Distribution Method

Distribution Architecture

Distribution Method

Speedup Equation

Distribution Scheme Results

Speedup

Speedup Equation

Distribution Method (Speedup)

Speedup Plot

Efficiency

Efficiency Equation

Distribution Method (Efficiency)

Efficiency Plot

Bottleneck?

Distribution Architecture

Bottleneck?

Distribution Architecture

Plugin System

Pathological Configurations

Example for need of plugin
Plugin Super Class

Provided Plugins

Gmsh Delaunay

Benefits of Plugins

Efficiency Equation

Conclusions

Conclusions

  1. Provided library performs Nth-order interpolation
  2. Parallel Implementation
  3. Plugin system

Conclusions

  1. Implementation is accurate
  2. Not a silver bullet
  3. For tested equations: Cubic Quartic, 32 Extra points

Future Work

Future Work

  1. Real world application/Multiphysics simulation
  2. More Performant Message Queuing Library (0MQ)
  3. Adaptive Parameter Selection
  4. Pathological Configuration

Acknowledgments

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