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Some Experiences on Parallel Finite Element Computations Using IBM/SP2

Some Experiences on Parallel Finite Element Computations Using IBM/SP2. Yuan-Sen Yang and Shang-Hsien Hsieh National Taiwan University Taipei, Taiwan, R.O.C. Contents. Parallel Substructure Method Three Issues : Mesh Partitioning Nodal Renumbering within Substructures

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Some Experiences on Parallel Finite Element Computations Using IBM/SP2

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  1. Some Experiences on Parallel Finite Element Computations Using IBM/SP2 Yuan-Sen Yang and Shang-Hsien Hsieh National Taiwan University Taipei, Taiwan, R.O.C.

  2. Contents • Parallel Substructure Method • Three Issues : • Mesh Partitioning • Nodal Renumbering within Substructures • Solution of Interface DOFs • Conclusions

  3. Parallel Substructure Method • Partition a structure into several substructures. • Assign each substructure to a processor. • Matrix assembly & static condensation within each substructure.

  4. Parallel Substructure Method (cont.) • Solve the displacements of interface DOFs. • Solve the displacements of internal DOFs in each substructure. • Perform force recovering in each substructure.

  5. Mesh Partitioning • Requirements • Automatic Partitioning • Handling regular & irregular meshes. • Balanced distribution of number of elements. • Minimization of number of interface nodes.

  6. Experiences (Mesh Partitioning) • GR, RST, METIS are used in this work. • Balanced distribution of number of elements is achieved. • Condensational load are unbalanced. RST

  7. Substructural Nodal Renumbering • Purpose: • To reduce the skyline of substructure matrix. • Constraint: • Interface nodes must be numbered after internal nodes • Reversed Cuthill-Mckee (RCM, Liu & Sherman 1975) is modified and used.

  8. Experiences (Substructure Nodal Renumbering) 30STORY. RST. With 4 processors • Help to Reduce the condensational loads. • Rarely balance the condensational loads among processors. Without Substructure Nodal Renumbering RST With modified RCM Substructure Nodal Renumbering

  9. Solution of Interface DOFs • Achieving high parallel efficiency for linear equation solver is not an easy task. • When NP increases NI increases Parallel Efficiency decreases

  10. Experiences (Solution of Interface DOFs) • In this work, a sequential direct method(Cholesky decomposition) is used. • NI is affected by both NP and the performance of the partitioning algorithm.

  11. Conclusions • Mesh partitioning • Computational loads of each processor is not necessarily proportional to its number of elements. • Minimization of interface nodes reduces the interface equations and usually improves the parallel efficiency. • Substructural nodal renumbering • Substructural nodal renumbering always reduces the condensational loads. • But rarely balance the condensational loads among procesors. • Parallel solution of interface DOFs • High-efficiency parallel solvers of interface equations are needed for improving the efficiency of parallel substructure method.

  12. Acknowledgement • This research is supported by the National Science Council of R.O.C., under the project Nos. NSC 86-2211-E-002-029 and NSC 87-2211-E-002-034. • The parallel computations are performed on IBM/SP2 comupters of National Center for High-performance Computing, Hsin-Chu, Taiwan, R.O.C.

  13. IBM/SP2 in NCHC • Model • IBM POWER2 SuperChip (P2SC) • Floating PeakPerformance • 480-MFLOPS • Memory • 128 Mbtyes per node

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