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Collaborator: K. Gärtner
Cooperation with: O. Schenk (Universität Basel, IFI, Switzerland)
Supported by: HP Integrity for Research Program
Description:
The work on PARDISO continued with respect to different topics, the central one was the introduction of matching algorithms and Bunch-Kaufman pivoting for indefinite symmetric linear systems. The problem is to enlarge the pivoting possibilities without introducing extraordinarily large fill-in or loosing the advantages of precomputed data dependency graphs during the parallel factorization. The present implementation uses two strategies (more exist) to construct a permutation to reduce fill-in and to make Bunch-Kaufman pivoting within the supernodes an efficient method: The permutation due to matching is split into cycles, and the cycles are broken up into smaller ones. The final permutation guarantees that supernodes are formed with respect to fill-in but include at least a cycle of length 2 or 3. Solving a symmetric linear system consisting of a two-cyclic matrix requires Bunch-Kaufman pivoting. In special circumstances regular matrices will still result in zero pivots and static pivoting. But for large classes of problems, serious progress was made. Users are now able to apply the proper level of stabilization according to the requirements of the special problem class.
With these extensions, a lot of new applications, especially optimization problems using interior point methods, can benefit from the faster factorization algorithm.
For personal academic use, the code is distributed now for many architectures via the net (see http://www.computational.unibas.ch/cs/scicomp/software/pardiso/).
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A classical PARDISO application area:
Sheet metal forming, Audi-TT door, green: acceptable plastic stretching,
problem requires the solution of symmetric indefinite linear systems.
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[Contents] | [Index] |