Implementing the Conjugate Gradient Method on a grid computer

We study two implementations of the Conjugate Gradient method for solving large sparse linear systems of equations on a heterogeneous computing grid, using GridSolve as grid middleware. We consider the standard CG algorithm of Hestenes and Stiefel, and as an alternative the Chronopoulos/Gear variant, a formulation that is potentially better suited for grid computing since it requires only one synchronisation point per iteration, instead of two for standard CG. The computational work is divided into tasks which are dynamically distributed over the available resources using a resource–aware data partitioning strategy. We present numerical experiments that show lower computing times and better speed–up for the Chronopoulos/Gear variant. We also identify bottlenecks and suggest improvements to GridSolve.