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IlO

the POD÷DEIM model in order to compare its accuracy to that of the RSW model.
For the full and POD+DEIM system simulations, the inputs are permitted to arrive
at the transition compartment, but in the RSW model, since this compartment is
absent, I redirect those inputs into the adjacent compartment on the strong fiber.

Table 4.1 shows the performance results of these simulations. It is not totally clear
whether or not the RSW model has improved upon the spike-capturing accuracy of
the POD÷DEIM model, but at least these results show that it is competitive. Note
that the location of xτ has an effect both on the simulation speed and on the accuracy.
Furthermore, I have used k_w = 10 for both RSW systems, and varying this parameter
may have an effect on the accuracy as well, and it will certainly affect the speed-up.

It appears at first glance that the RSW system is much slower than the POD+DEIM
system. However, profiling the code in MATLAB has shown that much extra time
is spent in directing the inputs to the proper strong and weak locations in vectors, a
task which is absent from the POD+DEIM code. Also, updating the “Hines” matrix
and performing Gaussian Elimination seems to take a bit longer, which is counterin-
tuitive. However, the expectation is that with a bit more optimization and perhaps
some very inexpensive pre-processing, the timings can be improved to be more in line
with what we would expect from the POD+DEIM simulations.

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