  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.
