report · JuSER (Forschungszentrum Jülich) · 2013

Performance analysis and comparison of parallel eigensolvers on Blue Gene architectures

Münchhalfen, J.F.

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Abstract

The solution of eigenproblems with dense, symmetric system matrices is a core task in many felds of computational science and engineering. As the problem complexity and thus the size of the matrices involved increases, the application of distributed memory supercomputer architectures and parallel algorithms becomes inevitable. Nearly all modern algorithms for eigensolving implement a tridiagonal reduction of the eigenproblem system matrix and a subsequentsolution of the tridigonalized eigenproblem. Additionally, back transformation of the eigenvectors is required if these are of interest. In the context of this thesis, implementations of two basically different approaches to the parallelsolution of eigenproblems were benchmarked, reviewed and compared with particular regard to their performance on the Blue Gene/P and Blue Gene/Q supercomputers JUGENE and JUQUEEN at the Forschungszentrum Jülich: ELPA, which implements an optimized version of the divide and conquer algorithm and Elemental which utilizes the PMRRR implementation of the MR3 algorithm. ELPA features two fundamentally different kinds of tridiagonalization, the standard one-stage and a two-stage approach. The comparision of thetwo-stage to the direct reduction was a primary concern in the performance analysis.

Cite this paper

APA 7

Münchhalfen, J. (2013). Performance analysis and comparison of parallel eigensolvers on Blue Gene architectures. JuSER (Forschungszentrum Jülich).

MLA 9

Münchhalfen, J.F. “Performance analysis and comparison of parallel eigensolvers on Blue Gene architectures.” JuSER (Forschungszentrum Jülich), 2013.

Chicago

Münchhalfen, J.F. 2013. “Performance analysis and comparison of parallel eigensolvers on Blue Gene architectures.” JuSER (Forschungszentrum Jülich).

Harvard

Münchhalfen, J. (2013) ‘Performance analysis and comparison of parallel eigensolvers on Blue Gene architectures’, JuSER (Forschungszentrum Jülich).

BibTeX

@article{munchhalfen2013performance,
  title = {{Performance analysis and comparison of parallel eigensolvers on Blue Gene architectures}},
  author = {Münchhalfen, J.F.},
  journal = {JuSER (Forschungszentrum Jülich)},
  year = {2013}
}

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