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

2. 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

4. Background - The White Rose Grid

5. Background – Elastohydrodynamic Lubricaton (EHL) Applications: High pressure contacts such as gears, valve trains, etc. Environmental Issues: Energy efficiency friction Durability wear

6. 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

7. 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

8. Typical Point Contact Solutions Film thickness Pressure Temperature

9. Grid-Enabled PSE - Overall Software Design gViz PSE (main) GridVisualiseSteer PSE (collaborator) gViz Simulation

10. Grid-Enabled PSE – Design (cont.) gViz PSE (main) GridVisualiseSteer PSE (collaborator) gViz Simulation

11. 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

12. 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).

13. Grid-Enabled PSE – Design (cont.) gViz PSE (main) GridVisualiseSteer PSE (collaborator) gViz Simulation

14. 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

15. Grid-Enabled PSE - Overall Software Design gViz PSE (main) GridVisualiseSteer PSE (collaborator) gViz Simulation

16. Grid-Enabled PSE – Design (cont.) gViz PSE (main) GridVisualiseSteer PSE (collaborator) gViz Simulation

17. Grid-Enabled PSE – Design (cont.) gViz GridVisualiseSteer gViz Simulation PSE (main) PSE (collaborator)

18. 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

19. Example of a typical IRIS Explorer map for the PSE:

20. Grid-Enabled PSE – Design (cont.) gViz PSE (main) GridVisualiseSteer PSE (collaborator) Simulation gViz

21. 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.

22. Hierarchical Parallelism (cont.)

23. 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 Np1612244896 Secs.512.093.350.029.317.615.1

24. 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!