Adaptive Analysis

The generic parallel h-adaptive procedure consists in the appropriate combination of the following components

- parallel finite element solver for the problem under consideration,
- parallel reliable posteriori error estimator providing a measure of the global and local error in a given norm to locate the regions that should be subjected to (de)refinement,
- refinement strategy translating the output from the error analysis into the desired distribution of mesh density,
- parallel or sequential mesh generator capable of (de)refinement according to the supplied mesh density distribution,
- mesh partitioner to decompose the mesh into balanced partitions,
- mapping operator which projects the current state of the model from the old mesh to the new (adapted) one.

Clearly, the efficiency of such a methodology depends not only on the efficiency of its individual components but also on the way how it is automated to minimize the user intervention. Note that mapping of the solution from the old mesh to the new one is not a trivial task because the meshes are decomposed into partitions that may overlap only partially or not at all. Moreover the number of partitions on the old mesh may be different from that on the new mesh. The mapping is therefore related to intensive data migration between the processors. Alternatively a static partitioning (decomposition that does not change during the whole analysis) may be adopted but in that case the dynamic load balancing cannot be applied.

*Daniel Rypl
2005-12-03*