School of Computing University of Leeds Computational PDEs Unit

1
School of Computing University of Leeds
Computational PDEs Unit

• A Grid-based approach to the validation and
  testing of lubrication models

Christopher Goodyer Martin Berzins Peter
Jimack Laurence Scales (Shell Global Solutions)
Funded by DTI/EPSRC e-Science Core Programme
(GR/S19486) and Shell Global Solutions
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School of Computing University of Leeds
Computational PDEs Unit

• A Grid-based approach to the validation and
  testing of lubrication models

Christopher Goodyer Martin Berzins Peter
Jimack Laurence Scales (Shell Global Solutions)
Funded by DTI/EPSRC e-Science Core Programme
(GR/S19486) and Shell Global Solutions
3
Presentation Overview

• Background
• The White Rose Grid
• Elastohydrodynamic lubrication (EHL)
• A Grid-enabled Problem Solving Environment (PSE)
• Simulation
• Grid Computing
• Visualisation and Computational Steering within a
  PSE
• Hierarchical Parallelism
• Implementation
• Parallel simulation example
• Conclusions

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Background - The White Rose Grid

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Background Elastohydrodynamic
Lubricaton (EHL)

• Applications
• High pressure contacts such as gears, valve
  trains, etc.
• Environmental Issues
• Energy efficiency ? friction
• Durability ? wear

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Background - EHL (cont.)

• Demanding mathematics and computer algorithms
• Very High Loads Small Areas
• High Pressures and Temperatures
• Deformation Glass-like Lubricant

Lubricant ? Experiment ? Theory ?
? ? Prediction ?
Computational Model
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Equations for the EHL Point Contact Problem

• System of equations in 2 space dimensions
• Reynolds Equation pressure distribution
• Film Thickness Equation deformation
• Force Balance Equation conservation law
• Lubricant model density, viscosity, temperature

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Typical Point Contact Solutions
Film thickness
Pressure
Temperature
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Grid-Enabled PSE - Overall Software Design
PSE (main)
PSE (collaborator)
Grid
Visualise
Steer
gViz
gViz
Simulation
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Grid-Enabled PSE Design (cont.)
PSE (main)
PSE (collaborator)
Grid
Visualise
Steer
gViz
gViz
Simulation
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Grid-Enabled PSE - Simulation

• Wish to find set of lubricant model parameters
  (e.g. viscosity, pressure, temperature
  coefficients) which best match observed data
• Typically at least 10 such parameters to optimise
• Observations for different loadings (3), ambient
  temperatures (2) and slideroll ratios (6)
• Nonlinear optimisation of

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Grid-Enabled PSE Simulation (cont)

• Each friction evaluation is an expensive EHL
  calculation
• Currently use a NAG library simplex algorithm for
  the multidimensional optimisation
• Scope for parallelism and use of Grid
• Could compute all 36 frictions in parallel at
  each R evaluation
• More efficient to use continuation in the
  slideroll parameters with 6 parallel processes
• Each of these 6 processes may themselves be
  implemented in parallel and launched on different
  Grid resources (each using multiple processors).

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Grid-Enabled PSE Design (cont.)
PSE (main)
PSE (collaborator)
Grid
Visualise
Steer
gViz
gViz
Simulation
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Grid-Enabled PSE Grid Computing

• Based upon use of the Globus Toolkit
• Module provided to interrogate a GIIS server to
  analyse available resources and their current
  status
• Job may be launched on selected resource(s) using
  Globus
• When job is spawned a connection is made back to
  the PSE (or Grid service) indicating which node
  of the Grid resource the simulation will be
  communicating from
• Although Grid certification is required to launch
  the simulation, use of gViz libraries allow
  collaborators around the world to see results of,
  or even steer, the simulation as it progresses

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Grid-Enabled PSE - Overall Software Design
PSE (main)
PSE (collaborator)
Grid
Visualise
Steer
gViz
gViz
Simulation
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Grid-Enabled PSE Design (cont.)
PSE (main)
PSE (collaborator)
Grid
Visualise
Steer
gViz
gViz
Simulation
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Grid-Enabled PSE Design (cont.)
PSE (main)
PSE (collaborator)
Grid
Visualise
Steer
gViz
gViz
Simulation
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Grid-Enabled PSE The PSE

• The complete PSE package is called GOSPEL (Grid
  Optimisation Software for Problems of
  Elastohydrodynamic Lubrication)
• It is built using NAGs IRIS Explorer software
  which uses a dataflow model
• The following IRIS Explorer map shows the three
  main modules
• GlobusSearch
• SteerGOSPEL
• VisualiseGOSPEL

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Example of a typical IRIS Explorer map for the
PSE
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Grid-Enabled PSE Design (cont.)
PSE (main)
PSE (collaborator)
Grid
Visualise
Steer
gViz
gViz
Simulation
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Hierarchical Parallelism

• Each friction calculation requires a costly EHL
  solve so this is implemented in parallel
• Parallel FAS multigrid
• Parallel multilevel multi-integration
• Each function evaluation requires 36 friction
  calculations so these are found in parallel
• Use of continuation means that six sets of six is
  far more efficient than 36 independent
  calculations.

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Hierarchical Parallelism (cont.)
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Hierarchical Parallelism (cont.)

• The following example shows typical speedups
  achieved
• The loss of efficiency is due to early completion
  of some of the continuation runs
• Different processor speeds
• Different computational costs when different
  loads are applied

Np 1 6 12 24 48 96
Secs. 512.0 93.3 50.0 29.3 17.6 15.1
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Conclusions

• Have demonstrated
• Solution of complex and computationally expensive
  EHL problems within outer optimization wrapper
• Hierarchical parallelism using Grid resources and
  software
• Use of Globus toolkit with MPI, NAG and gViz
  libraries
• Have also
• Implemented within a PSE to allow interactive
  visualization and computational steering (but not
  discussed here)
• Still to do
• Better load balancing
• More versatile applications e.g. actually
  designing lubricants!