A parallel implementation of overlapping Schwarz method for the dual reciprocity method

We present a parallel algorithm for the overlapping domain decomposition boundary integral equation method for two dimensional partial differential equations. In addition to the improvement of the ill-conditioning and the computational efficiency achieved by domain partitioning, using a parallel computer with p processors can offer up to p times efficiency. Assuming direct solution is used throughout, partitioning the domain into p subregions and employing a processor for each subproblem, overall, result in p2 times efficiency over using a single domain and a single processor, taking into account that a sequential algorithm of the underlying method can improve the computational efficiency at least p times over using a single domain. Some numerical results showing the efficiency of the parallel technique will be presented.