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Acceleration and Parallelization of ZENO/Walk-on-Spheres.

Derek Juba1, Walid Keyrouz1, Michael Mascagni1,2

  • 1Information Technology Laboratory National Institute of Standards and Technology, Gaithersburg, MD 20899.

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Summary

This study accelerates the Walk on Spheres (WoS) algorithm for nanoscale material property computation using Monte Carlo methods. Spatial data structures and parallel computing achieve significant speedups, enhancing ZENO software performance.

Keywords:
Monte Carlo MethodsWalk on Spheresk-D treenanomaterial propertiesparallelization

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Area of Science:

  • Computational physics
  • Materials science
  • Scientific computing

Background:

  • Monte Carlo methods (MCMs) are crucial for nanoscale material property computation.
  • The Walk on Spheres (WoS) algorithm, a type of MCM, is effective for solving partial differential equations (PDEs) but computationally intensive.
  • Accelerating MCMs is vital for advancing nanoscale simulations.

Purpose of the Study:

  • To accelerate the Walk on Spheres (WoS) algorithm within the ZENO software for nanoscale material property calculations.
  • To investigate the impact of spatial data structures on WoS performance.
  • To develop and evaluate a parallelized version of the WoS algorithm.

Main Methods:

  • Benchmarking various spatial data structures, including k-D trees, to optimize the computational geometry bottleneck in WoS.
  • Implementing multicore and cluster parallel versions of the WoS algorithm.
  • Comparing the performance of the accelerated algorithm against the original FORTRAN code.

Main Results:

  • Spatial data structures, particularly k-D trees, significantly accelerate the distance calculations required by WoS.
  • The parallel implementation exhibits linear strong scaling with the number of cores and compute nodes.
  • Up to a 4-order of magnitude speedup was achieved on a distributed system.

Conclusions:

  • Algorithmic acceleration using spatial data structures and parallelization dramatically improves the efficiency of the WoS algorithm for nanoscale simulations.
  • The enhanced ZENO software provides a powerful tool for faster and more accurate material property computation.
  • This work paves the way for more complex simulations in materials science.