The Divide-and-Conquer Framework: A Suitable Setting for the DDM of the Future

Abstract: This paper was prompted by numerical experiments we performed, in which algorithms already available in the literature (DVS-BDDM) yielded accelerations (or speedups) many times larger (more than seventy in some examples already treated, but probably often much larger) than the number of processors used. Based on these outstanding results, here it is shown that believing in the standard ideal speedup, which is taken to be equal to the number of processors, has limited much the performance goal sought by research on domain decomposition methods (DDM) and has hindered much its development, thus far. Hence, an improved theory in which the speedup goal is based on the Divide and Conquer algorithmic paradigm, frequently considered as the leitmotiv of domain decomposition methods, is proposed as a suitable setting for the DDM of the future.