A domain decomposition method for scattered data approximation on a distributed memory multiprocessor

Abstract

łThe problem of reconstructing a function f(x, y) from N experimental evaluations (x _i, y _i, f _i), i=1, ..., N irregularly distributed in the plane, has been considered for very large values of N. In this case the known local methods give the best sequential algorithms, but are not well suited for parallel implementation due to their excessively large arithmetic overhead. In this work we present a domain decomposition parallel method, especially studied for distributed memory multiprocessors which also achieves high efficiency as a sequential algorithm. In fact, it is based on the decomposition strategy already used in the local methods, but a particular decomposition in slightly overlapping regions and appropriate choice of the limited support weight functions has been realized in order to reduce arithmetic, communication and synchronization overheads. A good performance of the coarse grained parallel algorithm is then achieved by means of a dynamic arithmetic load- balance. Timings and efficiency results from a large experimentation carried out on a Hypercube iPSC/2 are given.

This work was conducted as part of the C.N.R. research contract n.90.00676.PF.69 ”Sistemi informatici e Calcolo Parallelo”