Parallelization of Irregular Problems Based on Hierarchical Domain Representation

Irregular problems require the computation of some properties for a set of elements that are irregularly distributed in a domain. The distribution may change at run time in a way that cannot be foreseen in advance. Most irregular problems satisfy a locality property because the properties of an element e depend on the elements that are "close" to e. We propose a methodology to develop a highly parallel solution based upon a load balancing strategy that respects locality because e and most of the elements close to e are mapped onto the same processing node. We also discuss the update of the mapping at run time to recover an unbalancing, together with strategies to acquire data on elements mapped onto other processing node. The proposed methodology is applied to the multigrid adaptive problem and some experimental results are discussed