Basic HTML version of Foils prepared 20 October 1997

Foil 46 Factor of Two in the Parallel O(N2) Algorithm

From Fox Presentation Fall 1995 CPS615 Basic Simulation Track for Computational Science -- Fall Semester 97. by Geoffrey C. Fox


Symmetry of force on particles: Fij = -Fji (Newton's Law of Action and Reaction!)
  • only half need to be computed
  • Sequentially this can easily be taken into account for one just does loops with sum over particles i, and then sums for force calculation over particles j <= i and then calculate algebraic form of Fij and then accumulates -- Force on i increments by Fij and Force on j decrements by Fij
Parallel version has two issues -- firstly one cannot use "owner-computes" rule directly and secondly one must worry about load blancing
Assuming for example that processors
assigned with block distribution in
column direction.
  • To calculate the force between
  • 2 particles will take N/Nproc iterations
  • in the longest running processor



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