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Linear Scaling Divide-and-conquer Electronic Structure Calculations for Thousand Atom Nanostructures

Lin-Wang Wang  (Lawrence Berkeley National Laboratory)
Byounghak Lee  (Lawrence Berkeley National Laboratory)
Hongzhang Shan  (Lawrence Berkeley National Laboratory)
Zhengji Zhao  (Lawrence Berkeley National Laboratory)
Juan Meza  (Lawrence Berkeley National Laboratory)
Erich Strohmaier  (Lawrence Berkeley National Laboratory)
David Bailey  (Lawrence Berkeley National Laboratory)
ACM Gordon Bell Finalists Session
Thursday,  11:30AM - 12:00PM
Room Ballroom G
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. 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 potential for petascale computation using the LS3DF method.
The full paper can be found in the IEEE Xplore Digital Library and ACM Digital Library
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