Here, we consider the single residual computation required by the integration
computations just described. Given a state vector 
, and
approximation for 
, we need to evaluate
. The exploitable concurrency available in this step is strictly
a function of the model equations. As defined, there are N equations in
this system, so we expect to use at best N computers for this step.
Practically, there will be interprocess communication between the process
rows, corresponding to the connectivity among the equations. This will place
an upper limit on 
(the number of row processes) that can be used
before the speed will again decrease: We can expect efficient speedup for
this step provided that the cost of the interprocess communication is
insignificant compared to the single-equation grain size. As estimated in
[Skjellum:90a], the granularity 
for the
Symult s2010 multicomputer is about fifty, so this implies about 450
floating-point operations per communication in order to achieve
90% concurrent efficiency in this phase.