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##

Parallel Method

As in our previous work on this system, the tridiagonal form for the
equations of motion forms the basis of the parallel method we use to
facilitate our calculations. For smaller , it is appropriate to use
the straightforward method of assigning blocks of the wave function
corresponding to a particular to a specific processor on
a parallel machine.[78] For large , it is much more
efficient to assign two states to each processor in such a way
that the load on each processor is nearly the same. To accomplish this, we
use the wrapping method described in Ref th:evi1996. Briefly,
this method takes into account the fact that for each state, , so that the size of the rotational basis decreases as
increases. Consider, for example, the even (spectroscopic) parity,
case using four processors. We assign the blocks corresponding
to the different states as follows:
processor ,
processor ,
processor , and
processor
. For an odd number of states, the problem is a bit more
difficult, but generally the first processor is singled out and assigned
only one state (either or , depending on
the parity) as well as I/O and other serial tasks. The only communication
between the processors arises from calculating the Coriolis terms, and is
small compared to e.g., the calculation of the vibrational terms in the
equations of motion.[1,78] In our calculations we use
MPI[79,80,81] to perform the communication between the
processors. See Refs. th:anth1998 and th:evi1996
for more details. Use of the ``wrapping method'', with two 's
per processor was made possible by the substantial savings in memory usage
through switching to the FBR-DVR approach (see Sec. IIB)
Because of memory considerations, we have not been able place more than
two states on a processor. The method easily generalizes, however, to
any *even* number of states per processor.

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Anthony J. H. M. Meijer
2000-10-05