school of computing university of leeds computational pdes unit a grid-based approach to the...

School of Computing University of Leeds Computational PDEs Unit

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

Christopher GoodyerMartin BerzinsPeter JimackLaurence Scales (Shell Global Solutions)

Funded by DTI/EPSRC e-Science Core Programme (GR/S19486) and Shell Global Solutions

School of Computing University of Leeds Computational PDEs Unit

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

Christopher GoodyerMartin BerzinsPeter JimackLaurence Scales (Shell Global Solutions)

Funded by DTI/EPSRC e-Science Core Programme (GR/S19486) and Shell Global Solutions

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

Background - The White Rose Grid

Background – Elastohydrodynamic

Lubricaton (EHL)

• Applications:High pressure contacts such as gears, valve trains, etc.

•Environmental Issues:Energy efficiency frictionDurability wear

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

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

0)()(

TH

XH

YP

YXP

X

22)'()'(

'')','(

00),(),(

yYxX

dydxyxPHYXgYXH

Typical Point Contact Solutions

Film thickness

PressureTemperatur

e

Grid-Enabled PSE - Overall Software Design

gViz

PSE (main)

Grid Visualise SteerPSE (collaborator)

gViz

Simulation

Grid-Enabled PSE – Design (cont.)

gViz

PSE (main)

Grid Visualise SteerPSE (collaborator)

gViz

Simulation

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 slide:roll ratios (6)

• Nonlinear optimisation of

36

1

exp 2)(

jj

numjF FFR

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 slide:roll 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).

Grid-Enabled PSE – Design (cont.)

gViz

PSE (main)

Grid Visualise SteerPSE (collaborator)

gViz

Simulation

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

Grid-Enabled PSE - Overall Software Design

gViz

PSE (main)

Grid Visualise SteerPSE (collaborator)

gViz

Simulation

Grid-Enabled PSE – Design (cont.)

gViz

PSE (main)

Grid Visualise SteerPSE (collaborator)

gViz

Simulation

Grid-Enabled PSE – Design (cont.)

gViz

Grid Visualise Steer

gViz

Simulation

PSE (main)

PSE (collaborator)

Grid-Enabled PSE – The PSE

• The complete PSE package is called GOSPEL (Grid Optimisation Software for Problems of Elastohydrodynamic Lubrication)

• It is built using NAG’s IRIS Explorer software which uses a dataflow model

• The following IRIS Explorer map shows the three main modules:– GlobusSearch

– SteerGOSPEL

– VisualiseGOSPEL

Example of a typical IRIS Explorer map for the PSE:

Grid-Enabled PSE – Design (cont.)

gViz

PSE (main)

Grid Visualise SteerPSE (collaborator)

Simulation

gViz

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.

Hierarchical Parallelism (cont.)

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

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!