A Partitioning Strategy for Nonuniform Problems on Multiprocessors

Abstract

We consider the partitioning of a problem on a domain with unequal work estimates in different subdomains in a way that balances the workload across multiple processors. Such a problem arises for example in solving partial differential equations using an adaptive method that places extra grid points in certain subregions of the domain. We use a binary decomposition of the domain to partition it into rectangles requiring equal computational effort. We then study the communication costs of mapping this partitioning onto different multiprocessors: a mesh- connected array, a tree machine, and a hypercube. The communication cost expressions can be used to determine the optimal depth of the above partitioning.