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

Authors:
Mathieu Luisier;Gerhard Klimeck;Andreas Schenk;Wolfgang Fichtner;Timothy B. Boykin
Affiliations:
Network for Computational Nanotechnology, Purdue University, West Lafayette, USA 47907;Network for Computational Nanotechnology, Purdue University, West Lafayette, USA 47907;Integrated Systems Laboratory, ETH Zurich, Zurich, Switzerland CH-8092;Integrated Systems Laboratory, ETH Zurich, Zurich, Switzerland CH-8092;Department of Electrical and Computer Engineering, The University of Alabama in Huntsville, Huntsville, USA 35899
Venue:
Euro-Par '08 Proceedings of the 14th international Euro-Par conference on Parallel Processing
Year:
2008

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Abstract

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 4012328 (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.