Abstract

CHAPTER 3. BIFURCATION ANALYSIS 57
bordering method. This is because the bordering method’s coefficient matrix is the
Jacobian matrix W ′ ( f) which will be going singular at turning points.
3.7 Parallelization of Simulator
Since LOCA has been developed to run with both serial and parallel applications
and adding grid points to enhance the accuracy of the simulation would substan-
tially increase computational time, we were motivated to parallelize the simulator.
Therefore, we had to determine how we would split apart the f vector and the W ( f)
evaluation across the different processors. We decided to divide the f vector across
the processors by the spatial variable x. This meant each processor had a contiguous
block of x-space, with each processor owning all of the possible k values for each x
grid point it had. This makes computing integrals in k-space a completely parallel
process, with no communication between processors required, but the integral and
derivative term in x-space will require communication between the processors. One
could have done the opposite, where each processor gets a continugous block of k-
space, with each processor owning all of the possible x values for each k grid point it
had. In this case, computing the derivative and integral in x-space would be trivial
while requiring communication between processors to compute the k-space integrals.
We chose the way we distributed the data between the processors because there are
more k-space integrals to compute, and they are the most computationally intensive
part of the simulation.