A Parallel Sparse Linear Solver for Nearest-Neighbor Tight-Binding Problems

  • Mathieu Luisier
  • Gerhard Klimeck
  • Andreas Schenk
  • Wolfgang Fichtner
  • Timothy B. Boykin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5168)


This paper describes an efficient sparse linear solver for block tri-diagonal systems arising from atomistic device simulation based on the nearest-neighbor tight-binding method. The algorithm is a parallel Gaussian elimination of blocks corresponding to atomic layers instead of single elements. It is known in the physics community as the renormalization method introduced in 1989 by Grosso et al, [Phys. Rev. B 40 12328 (1989)]. Here, we describe in details the functionality of the algorithm and we show that it is faster than direct sparse linear packages like Pardiso, MUMPS or SuperLU_DIST and that it scales well up to 512 processors.


Atomic Layer Gaussian Elimination Diagonal Block Cyclic Reduction Speed Improvement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Mathieu Luisier
    • 1
  • Gerhard Klimeck
    • 1
  • Andreas Schenk
    • 2
  • Wolfgang Fichtner
    • 2
  • Timothy B. Boykin
    • 3
  1. 1.Network for Computational NanotechnologyPurdue UniversityWest LafayetteUSA
  2. 2.Integrated Systems LaboratoryETH ZurichZurichSwitzerland
  3. 3.Department of Electrical and Computer EngineeringThe University of Alabama in HuntsvilleHuntsvilleUSA

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