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S. Boeriu 1 and J.C. Bruch, Jr. 2 1 Center for Computational Science and Engineering

Performance analysis tools applied to a finite adaptive mesh free boundary seepage parallel algorithm. S. Boeriu 1 and J.C. Bruch, Jr. 2 1 Center for Computational Science and Engineering 2 Department of Mechanical and Environmental Engineering and Department of Mathematics

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S. Boeriu 1 and J.C. Bruch, Jr. 2 1 Center for Computational Science and Engineering

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  1. Performance analysis tools applied to a finite adaptive mesh free boundary seepage parallel algorithm S. Boeriu1 and J.C. Bruch, Jr.2 1Center for Computational Science and Engineering 2Department of Mechanical and Environmental Engineering and Department of Mathematics University of California, Santa Barbara http://www.engineering.ucsb.edu/~hpscicom

  2. Acknowledgements Thismaterial is based upon work supported by the National Science Foundation under Grant #0086262. This research was supported in part by NSF cooperative agreement ACI-9619020 through computing resources provided by the National Partnership for Advanced Computational Infrastructure at the San Diego Supercomputer Center. http://www.npaci.edu/Horizon/guide_linked/bh_tools_txt.html

  3. Outline of Presentation • Introduction (Physical problem) • Problem formulation • Fixed domain formulation • Numerical algorithm • Test case • Performance tools and considerations a. VAMPIR b. PARAVER • Diagnostic example • Conclusions

  4. Physical problem Figure 1. Seepage through a rectangular dam.

  5. Simplifying assumptions • The soil in the flowfield is homogeneous and isotropic • Capillary and evaporation effects are neglected • The flow obeys Darcy’s Law • Two-dimensional • Steady state

  6. Mathematical formulation • Darcy’s Law: • Potential Function: Velocity Components: Continuity Equation: Irrotationality Condition: Cauchy-Riemann Equations: Laplace’s Equations:

  7. Problem formulation Figure 2. Mathematical formulation of physical problem.

  8. Extension of solution domain The solution domain is extended to the known region Then extend continuously to be defined on by setting

  9. This yields in the sense of distributions where

  10. Fixed domain formulation Figure 3. Fixed domain mathematical formulation.

  11. Numerical Algorithm A minimization problem can be formulated in terms of the functional where ais a bilinear form, continuous, symmetric, positive definite on R and i.e.,

  12. The functional J has one and only one minimum on a closed convex set. The minimum is found using the following algorithm:

  13. Finite Element Error Analysis Adaptive Mesh Finite Element Analysis (FEA) General Equation for FEA:

  14. Error Analysis Error Definition: where is the approximation of the exact solution ; is the calculated of an element (constant); is the shape function; and

  15. Averaging Technique: Error Estimate in an Element:

  16. Error Norm of the Whole Computation Domain: Percentage Error:

  17. Local Mesh Refinement Desired Criteria: Desired Local Error Criteria: Error Ratio: New Element Size:

  18. Mesh Refinement

  19. Test case

  20. Results

  21. Figure 4. Domain decomposition for Pass 4 of Case 1.

  22. Figure 5. Speedup for Case 1.

  23. Performance tools and considerations The parallel program is monitored while it is executed. Monitoring produces performance data that is interpreted in order to reveal areas of poor performance. The program is then altered and the process is repeated until an acceptable level of performance is reached.

  24. VAMPIR(Visualization and Analysis of MPI Resources – 2.0) • VAMPIR 2.0 is a post-mortem trace visualization tool from Pallas GmbH http://www.pallas.com It uses the profile extensions to MPI and permits analysis of the message events where data is transmitted between processors during execution of a parallel program. It has a convenient user-interface and an excellent zooming and filtering. Global displays show all selected processes.

  25. Global Timeline: detailed application execution over time axis • Activity Chart: presents per-process profiling information • Summaric Chart: aggregated profiling information • Communication Statistics: message statistics for each process pair • Global Communication Statistics: collective operations statistics • I/O Statistics: MPI I/O operation statistics • Calling Tree: global dynamic calling tree

  26. PARAVER(Parallel Program Visualization and Analysis Tool) • PARAVER is a flexible parallel program visualization and analysis tool based on an easy-to-use Motif GUI (graphical user interface) PARAVER was developed to respond to the basic need to have a qualitative perception of the application behavior by visual inspection and then to be able to focus on the detailed quantitative analysis of the problems.

  27. Paraver (Parallel Program Visualization and Analysis Tool) • Powerful flexible parallel program visualization tool based on an easy-to-use Motif GUI (graphical user interface) • Developed by : European Center for Parallelism of Barcelona (CEPBA) Universitat Politecnica de Catalunya http://www.cepba.upc.es/

  28. Paraver is designed to visualize and analyze - Communication and load balance - Combining OpenMP and MPI - Hardware performance and counters • Usage - Compile programs with special libraries - Run programs to produce trace files - View and analyze traces - Designed to help in program understanding and optimization

  29. Inefficient programming example • Load imbalance (inefficient memory use) • TLB (translation lookaside buffer) misses

  30. Figure 6. Stage 1 – Processor 0 – Mesh Map

  31. Figure 7. Stage 1 – Processor 3 – Mesh Map

  32. Figure 8. Stage 1 – VAMPIR – Activity Chart

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