NDLI: Advancing Large Scale Many-Body QMC Simulations on GPU Accelerated Multicore Systems

Content Provider	IEEE Xplore Digital Library
Author	Tomas, A. Chia-Chen Chang Scalettar, R. Zhaojun Bai
Copyright Year	2012
Abstract	The Determinant Quantum Monte Carlo (DQMC) method is one of the most powerful approaches for understanding properties of an important class of materials with strongly interacting electrons, including magnets and superconductors. It treats these interactions exactly, but the solution of a system of $N$ electrons must be extrapolated to bulk values. Currently $N \approx 500$ is state-of-the-art. Increasing $N$ is required before DQMC can be used to model newly synthesized materials like functional multilayers. DQMC requires millions of linear algebra computations of order $N$ matrices and scales as $N^3$. DQMC cannot exploit parallel distributed memory computers efficiently due to limited scalability with the small matrix sizes and stringent procedures for numerical stability. Today, the combination of multisocket multicore processors and GPUs provides widely available platforms with new opportunities for DQMC parallelization. The kernel of DQMC, the calculation of the Green's function, involves long products of matrices. For numerical stability, these products must be computed using graded decompositions generated by the QR decomposition with column pivoting. The high communication overhead of pivoting limits parallel efficiency. In this paper, we propose a novel approach that exploits the progressive graded structure to reduce the communication costs of pivoting. We show that this method preserves the same numerical stability and achieves 70\% performance of highly optimized {\tt DGEMM} on a two-socket six-core Intel processor. We have integrated this new method and other parallelization techniques into QUEST, a modern DQMC simulation package. Using 36 hours on this Intel processor, we are able to compute accurately the magnetic properties and Fermi surface of a system of $N=1024$ electrons. This simulation is almost an order of magnitude more difficult than $N \approx 500$, owing to the $N^3$ scaling. This increase in system size will allow, for the first time, the computation of the magnetic and transport properties of layered materials with DQMC. In addition, we show preliminary results which further accelerate DQMC simulations by using GPU processors.
Starting Page	308
Ending Page	319
File Size	2473622
Page Count	12
File Format	PDF
ISBN	9781467309752
ISSN	15302075
DOI	10.1109/IPDPS.2012.37
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-05-21
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Computational modeling Matrix decomposition Multicore processing Program processors Materials Lattices Green products GPU Quantum Monte Carlo QRP multicore
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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