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Tool-supported parallelization of finite-element applications


The aim of the project PARFEM is a tool-supported parallelization of finite-element applications and their implementation on different architectures. Important questions are general parallelization strategies, scheduling problems and how to solve the large, sparse, symmetric and positive definite systems of linear equations.


For the solution of large, sparse systems of equations, theg Central Institute for Applied Mathematics at Research Centre Juelich considers the method of conjugate gradients. This algorithm offers good potential for parallelism. For better performance, different preconditioning techniques (e.g. polynomial preconditioning, incomplete Cholesky-factorization) are investigated.

Finally the algorithms should be integrated in the finite-element program PERMAS.

Partners / Grants

  • Daimler-Benz AG, Stuttgart
  • Gesellschaft für Mathematik und Datenverarbeitung, Birlinghoven
  • Intes GmbH, Stuttgart
  • Pallas GmbH, Brühl
  • University Rostock
  • Institute for safety research and reactor techniques, Forschungszentrum Jülich
  • Central Institute for Applied Mathematics, Forschungszentrum Jülich

The project was funded by the German Federal Ministry of Education and Research (BMBF).

The grant period was March 1994 until December 1996.

Status and Results

The project was completed in schedule.

The optimization and parallelization of the preconditioning-methods as the main factor in the development of the CG-algorithm was achieved using the domain-decomposition technique and message-passing programming. First the graph-oriented concept of parallelization had to show its efficiency for various solvers, second the programming tools had to be evaluated for the CG-method. The implementation of the Block-Cholesky-preconditioned CG-method exists of two variants. The first variant uses the self-parallelising tools, the second one, a stand-alone-solver, bypasses the scheduling-system by using a PERMAS-interface. The developed tools for parallelising work efficiently, but with the CG-solver as application performance is poor. In contrast, the stand-alone solver integrated in PERMAS shows the possible numerical power of the parallel CG-method.


  • PARFEM - Werkzeugunterstützte Parallelisierung von Finite-Elemente Anwendungen
    HPSC 95, 11.-14. September 1995, Jülich
  • Preconditioned CG methods for sparse matrices on massively parallel machines
    Basermann, A.; Reichel,B.; Schelthoff Ch. (1995)
    Parallel Computing 23 (1997), 381-398,
    DOI: 10.1016/S0167-8191(97)00005-7
    (also Technical Report IB-9531, December 1995, 16 Pages)
  • PARFEM - Werkzeugunterstützte Parallelisierung von Finite-Elemente Anwendungen
    HPSC 97, 25.-26. Februar 1997, München