4.2.4 Inductive Continuation

The above process repeats until all particles have been emitted and absorbed. There are several important factors to observe in order to achieve good parallel efficiency:

• The vector (or parallel) lengths should be kept sufficiently long so as to yield good efficiency. Note that, as particles pass the hierarchical tests (i.e., traverse the ``sieves''), the vector length tends to decrease. To ensure good overall efficiency, the shortest vector length should be long enough to obtain good efficiency. A suitable vector length is usually determined empirically and depends upon: (1) the input parameters (geometry and material properties) and (2) architecture.

• It is important to maintain long vector lengths by re-filling the vectors with new emission as particles ``die off.''

• A ``tail'' will inevitably exist at the end of this process, as the particles remaining after the last emission will need to be traced through enough events for them all to ``die off.'' Zhong and Kalos [4] have identified this as the ``straggler'' problem. We are fortunate that it exists only at the end of our problem. In some physical situations, stragglers exist during each event step, requiring synchronization between events.