Biomedical Engineering Reference
In-Depth Information
Figure 12.
The RED element is in the middle, and its 6 neighbors (west, east, south, north,
bottom, and top) have the sum of indices different by 1 from the middle one, so they are all
BLACK elements. See attached CD for color version.
same strategy the residuals
R
(
l
)
not after every RED-BLACK iteration, since it is
time consuming in itself, but after every ten RED-BLACK iterations. Fulfiling the
stopping criterion for the SOR iterations, we get an approximate solution in the
new time step. In checking the stopping condition (23) of the overall segmentation
process, we have to employ in a similar way the procedure MPI Allreduce in
evaluation of the L
2
norm of difference of subsequent time step solutions.
Using the PARAVER software, in Figures 16-19 we visualize the run of our
parallel program, computing just one time step of the method on four proces-
sors. In Figure 16 we can see in green color the time spent for the MPI Init and
MPI Finalize functions. In blue color we can see the running time of the pro-
gram outside the MPI subroutines. First there is the parallel reading of the image,
computing
g
T
coefficients and construction of the initial segmentation function,
and then we can see 50 iterations of the RED-BLACK SOR method, indicated
by yellow lines corresponding to data exchanges. Figure 17 shows the zoom of
the previous visualization at the start of the iteration process. The time spent
in the MPI Allreduce subroutine by every process is visualized in orange. This
corresponds to a synchronization of all processes at the first computation of ini-
tial residual before starting iterations of the RED-BLACK SOR method. Next,
MPI Allreduce we can see almost on the right end of the picture, when the residual
after ten RED and ten BLACK iterations is computed. Figure 18 zooms in on this
part of the parallel run. Together with MPI Allreduce in orange, we can see the
MPI Wait procedure in red, the data exchanges expressed by the yellow lines, and
