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Parallelization Strategy

The adopted parallelization strategy is based on a mesh partitioning. The partitioning should take into account following aspects to be optimally load-balanced: Generally, two dual partitioning concepts for the parallelization of explicit integration schemes exist. With respect to the character of a cut dividing the problem mesh into partitions, one can distinguish between node-cut and element-cut concepts. In the presented study, both approaches will be investigated. The node-cut approach is based on a unique assignment of individual elements to partitions. A node is then either assigned to a partition (local node), if it is surrounded exclusively by elements assigned to that partition, or it is shared by several partitions (shared node), if it is incident to elements owned by different partitions (see Fig. 1). In the element-cut approach, the nodes of the mesh are uniquely assigned to partitions. An element is then either assigned to a partition (local element), if all its nodes are lying on that partition, or it is duplicated on several partitions (duplicated element), if its nodes are belonging to different partitions. The geometry of a duplicated element is represented on a particular partition by local node(s) assigned to the same partition and by node(s) owned by a different partition (so called remote-copy node(s), see Fig. 2). While the first partitioning scheme can be interpreted as mesh decomposition by cuts leading through shared nodes of the mesh but not crossing any element (node-cut strategy), the second one is represented by cuts crossing the duplicated elements of the mesh but avoiding the nodes (element-cut strategy). The duality between both strategies with respect to the cut and assignment and duplication/sharing of the nodes and elements has been shown in [6]. Note, however, that the strategies are not equal from the computational point of view because of a different computational complexity associated with nodes and elements, respectively. Since the computation on an element is typically more demanding than on a node, the element-cut strategy, yielding the duplication of elements along the partition cuts, is less efficient.

Nonlocal constitutive models work with quantities which are typically obtained by the averaging over a specific region (nonlocal quantities). This averaging becomes difficult near the inter-partition boundary because some of the data required by the averaging algorithm are stored on different partitions. To tackle this problem, an additional communication between the partitions must be realized. As it will be explained in Section 6, a data exchange related to the averaging over the inter-partition boundary would result in an excessive fine grain communication. Therefore a modification of the described partitioning strategies will be considered as an alternative and efficient solution. The modification consists in an extension of each partition by a band of mirrored elements (remote-copy elements), assigned to surrounding (but not always only adjacent) partitions and by remote nodes, incident to these elements. Both the remote elements and nodes are treated as a copy of the original at the corresponding partition. The band must be wide enough to enable averaging on local and duplicated elements at a given partition, using only the local and remote elements integration points (which are available on that particular partition) without explicitly accessing the off-partition data.



Next: Local Constitutive Model Strategy Up: Top Previous: Constitutive Model

Daniel Rypl
2005-12-03