Linearly scaling 3D fragment method for large-scale electronic structure calculations

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Linearly scaling 3D fragment method for large-scale electronic structure calculations

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Conference on High Performance Networking and Computing archive
Proceedings of the 2008 ACM/IEEE conference on Supercomputing - Volume 00 table of contents

Austin, Texas

SECTION: ACM Gordon Bell finalists table of contents

Article No. 65

Year of Publication: 2008

ISBN:978-1-4244-2835-9

Authors

Lin-Wang Wang	Lawrence Berkeley National Laboratory, Berkeley, CA
Byounghak Lee	Lawrence Berkeley National Laboratory, Berkeley, CA
Hongzhang Shan	Lawrence Berkeley National Laboratory, Berkeley, CA
Zhengji Zhao	Lawrence Berkeley National Laboratory, Berkeley, CA
Juan Meza	Lawrence Berkeley National Laboratory, Berkeley, CA
Erich Strohmaier	Lawrence Berkeley National Laboratory, Berkeley, CA
David H. Bailey	Lawrence Berkeley National Laboratory, Berkeley, CA

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IEEE Press Piscataway, NJ, USA

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ABSTRACT

We present a new linearly scaling three-dimensional fragment (LS3DF) method for large scale ab initio electronic structure calculations. LS3DF is based on a divide-and-conquer approach, which incorporates a novel patching scheme that effectively cancels out the artificial boundary effects due to the subdivision of the system. As a consequence, the LS3DF program yields essentially the same results as direct density functional theory (DFT) calculations. The fragments of the LS3DF algorithm can be calculated separately with different groups of processors. This leads to almost perfect parallelization on over one hundred thousand processors. After code optimization, we were able to achieve 60.3 Tflop/s, which is 23.4% of the theoretical peak speed on 30,720 Cray XT4 processor cores. In a separate run on a BlueGene/P system, we achieved 107.5 Tflop/s on 131,072 cores, or 24.2% of peak. Our 13,824-atom ZnTeO alloy calculation runs 400 times faster than a direct DFT calculation, even presuming that the direct DFT calculation can scale well up to 17,280 processor cores. These results demonstrate the applicability of the LS3DF method to material simulations, the advantage of using linearly scaling algorithms over conventional O(N³) methods, and the potential for petascale computation using the LS3DF method.

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