Finite element methods on parallel and vector computers application in fluid dynamics
The experiences described in this paper show that finite element methods can be vectorized efficiently, though they are slightly penalized by the need of indirect addressing. The extension to 3-D problems is currently under investigation. The main question is to find a graph coloring algorithm to get a small number of colors, with enough elements in each color. A useful heuristic is to freeze in advance the maximal size of each group, thus the vector length. Implicit schemes without storage of the matrix are also examined, to get a good tradeoff between memory requirements and CPU time.
Concerning the parallel algorithms, the subdomain approach seems more efficient. But the microtasking approach should give better results on larger problems, with a larger granularity. It is easier to implement and does not require a preliminary partitionning.
However, we plan to investigate partitionning methods, with more general configurations (variable number of neighbors), using general graph separation algorithms. Simulated annealing techniques are also considered to optimize locally the separator length.
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