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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 $J$, it is appropriate to use the straightforward method of assigning blocks of the wave function corresponding to a particular $\Omega$ to a specific processor on a parallel machine.[78] For large $J$, it is much more efficient to assign two $\Omega$ 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 $\Omega$ state, $j \ge
\Omega$, so that the size of the rotational basis decreases as $\Omega$ increases. Consider, for example, the even (spectroscopic) parity, $J=7$ case using four processors. We assign the blocks corresponding to the different $\Omega$ states as follows: $\Omega = 0,7 \rightarrow$ processor $0$, $\Omega = 1,6 \rightarrow$ processor $1$, $\Omega = 2,5
\rightarrow$ processor $2$, and $\Omega = 3,4 \rightarrow$ processor $3$. For an odd number of $\Omega$ states, the problem is a bit more difficult, but generally the first processor is singled out and assigned only one $\Omega$ state (either $\Omega=0$ or $\Omega=1$, 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 $\Omega$'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 $\Omega$ states on a processor. The method easily generalizes, however, to any even number of $\Omega$ states per processor.


next up previous
Next: Initial Conditions Up: Theory and Computational details Previous: Hamiltonian, Propagation, and Analysis
Anthony J. H. M. Meijer 2000-10-05