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Exercise 13: Some thoughts on adaptive mesh generation.

Another exercise involves fixing the number of nodes to the maximum number and then moving the nodes so that they are positioned in the optimal locations (the so-called r method or relocation method). Still another possibility is to use an de-refinement strategy, in which regions of the discretized domain that were too finely meshed in the original mesh can be ``unrefined'' and help balance the total number of degrees of freedom. At some point, however, for most large three-dimensional problems, one must face the option of parallelizing the algorithms so that they can be run on either a distributed system of high-end workstations or a massively parallel machine. The use of such techniques for adaptive mesh generation is just in its infancy, but is certainly a topic of considerable importance to researchers who work on large-scale finite element systems.

To find out more about parallel adaptive refinement methods and adaptive methods in general, see [45,34,39,40,42].