Performance of dynamic load balancing algorithms for unstructured mesh calculations

If a finite element mesh has a sufficiently regular structure, it is easy to decide in advance how to distribute the mesh among the processors of a distributed-memory parallel processor, but if the mesh is unstructured, the problem becomes much more difficult. The distribution should be made so that each processor has approximately equal work to do, and such that communication overhead is minimized. If the mesh is solution-adaptive, i.e. the mesh and hence the load balancing problem change discretely during execution of the code, then it is most efficient to decide the optimal mesh distribution in parallel. In this paper three parallel algorithms, Orthogonal Recursive Bisection (ORB), Eigenvector Recursive Bisection (ERB) and a simple parallelization of Simulated Annealing (SA) have been implemented for load balancing a dynamic unstructured triangular mesh on 16 processors of an NCUBE machine. The test problem is a solution-adaptive Laplace solver, with an initial mesh of 280 elements, refined in seven stages to 5772 elements. We present execution times for the solver resulting from the mesh distributions using the three algorithms, as well as results on imbalance, communication traffic and element migration. The load balancing itself is fastest with ORB, but a very long run of SA produces a saving of 21% in the execution time of the Laplace solver. ERB is only a little slower than ORB, yet produces a mesh distribution whose execution time is 15% faster than ORB. C3P 913 June 1990