The divide-and-conquer framework: a suitable setting for domain decomposition methods of the future

Abstract

This paper was prompted by numerical experiments we performed, in which algorithms that Ismael Herrera Research Group previously developed (the DVS-BDDC) and are already available in the literature, 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 such outstanding results, this paper shows that believing that the ideal speedup is equal to the number of processors, has limited the performance-goal sought by researchers 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.