Accelerating Sparse Arithmetic in the Context of Newton’s Method for Small Molecules with Bond Constraints

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• 关键词：Newton’s method ; Non ; linear equations ; Molecular dynamics ; Constraints ; SHAKE ; RATTLE ; LINCS ; Compiled code approach ; Vector level parallelism ; Vectorizing compiler ; SIMD
• 刊名：Lecture Notes in Computer Science
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：9573
• 期：1
• 页码：160-171
• 全文大小：299 KB
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• 作者单位：Carl Christian Kjelgaard Mikkelsen (19)
  Jesús Alastruey-Benedé (20)
  Pablo Ibáñez-Marín (20)
  Pablo García Risueño (21) (22) (23)
  
  19. Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden
  20. Instituto Universitario de Investigación en Ingeniería de Aragón (I3A), Universidad de Zaragoza, Zaragoza, Spain
  21. Institut für Physik, Humboldt Universität zu Berlin, Berlin, Germany
  22. Fritz-Haber Institut (MPG), Berlin, Germany
  23. Instituto de Biocomputación y Física de Sistemas Complejos, Zaragoza, Spain
  
• 丛书名：Parallel Processing and Applied Mathematics
• ISBN：978-3-319-32149-3
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349

文摘

Molecular dynamics is used to study the time evolution of systems of atoms. It is common to constrain bond lengths in order to increase the time step of the simulation. Here we accelerate Newton’s method for solving the constraint equations for a system consisting of many identical small molecules. Starting with a modular and generic base code using a sequential data layout, we apply three different optimization techniques. The compiled code approach is used to generate subroutines equivalent to a single step of Newton’s method for a user specified molecule. Differing from the generic subroutines, these specific routines contain no loops and no indirect addressing. Interleaving the data describing different molecules generates vectorizable loops. Finally, we apply task fusion. The simultaneous application of all three techniques increases the speed of the base code by a factor of 15 for single precision calculations.