Optimized partitioning of unstructured finite element meshes

Abstract

We address the problem of automatic partitioning of unstructured finite element meshes in the context of parallel numerical algorithms based on domain decomposition. A two-step approach is proposed, which combines a direct partitioning scheme with a non-deterministic procedure of combinatorial optimization. In contrast with previously published experiments with non-deterministic heuristics, the optimization step is shown to produce high-quality decompositions at a reasonable compute cost. We also show that the optimization approach can accommodate complex topological constraints and minimization objectives. This is illustrated by considering the particular case of topologically one-dimensional partitions, as well as load balancing of frontal subdomain solvers. Finally, the optimization procedure produces, in most cases, decompositions endowed with geometrically smooth interfaces. This contrasts with available partitioning schemes, and is crucial to some modern numerical techniques based on domain decomposition and a Lagrange multiplier treatment of the interface conditions.

Parallel Dynamic Graph Partitioning for Adaptive Unstructured Meshes

“…Typically the cost function used is simply the total weight of cut edges, |E c |, and then the gain expresses the change in |E c |. More recently, however, there has been some debate about the most important quantity to minimize and in [14], Vanderstraeten et al demonstrated that it can be extremely effective to vary the cost function based on a knowledge of the solver. Meanwhile, in [17] we showed that the architecture of the parallel machine and how the partition is mapped down onto its communications network can also play an important role.…”

Iterative mesh partitioning optimization for parallel nonlinear dynamic finite element analysis with direct substructuring

“…Vanderstraeten et al (Vanderstraeten and Keunings, 1995;Vanderstraeten et al, 1996) have proposed several two-step mesh partitioning approaches. These approaches first produce a partitioning result via an initial partitioning algorithm.…”

“…They are based on graph partitioning techniques (Pothen, 1997), which have been used extensively for parallel scientific computations. Herein, a finite element mesh is transferred to a Communication Graph (C-Graph), which is similar to the diagonal dual graph used by Vanderstraeten and Keunings (1995), and then partitioned via one of the mesh partitioning packages. Details on the transformation from a finite element mesh to a C-Graph can be found in Hsieh et al (1995).…”

Parallel Implementation of DSMC Using Unstructured Mesh

“…Thus, domain decomposition in DSMC can become very efficient by taking advantage of the success in graph partitioning. Related descriptions and reviews of graph partitioning can be found in Kernighan and Lin (1970), Barnard and Simin (1994), Hendrickson and Leland (1994), Karypis and Kumar (1995), Vanderstraeten and Keunings (1995), Walshaw et al (1995), Vanderstraeten et al (1996) and Robinson (1998), and are not repeated here. There are, however, two graph partitioners available in the public domain worthy of mentioning, and they are described in the following.…”