Optimal Communication Interval for Parallel Adaptive Integration

Abstract

Parallelization of integration routines based on adaptive subdivision strategies is inherently di.cult. Hard subregions turning up on one node have to be redistributed to other nodes as fast as possible. Determining the optimal communication frequency is crucial, otherwise the program either wastes time with excessive communication, or only few nodes can tackle important regions.

We simulate numerical integration on parallel computers, depending on parameters like integrand type, communication protocol or number of processing nodes. Determining the optimal communication interval for each test case yields insight into the parameters determining it in general.