Acceleration and Parallelization of ZENO/Walk-on-Spheres

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.