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Adaptive Analysis

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

Initially, the problem is discretized using the mesh generator, optionally taking into account a-priori error assessment (typically based on the user experience). If a sequential generator is employed the resulting mesh is then decomposed into appropriate number (usually specified by the user) of well balanced partitions. In the case of a parallel mesh generator, a parallel version of the mesh partitioner may be used to repartition the mesh if the original decomposition produced by the mesh generator is not satisfactory. The problem is then analyzed using the parallel finite element solver. After each step of the nonlinear solution, the error estimation is invoked. If the global relative error exceeds the prescribed value the refinement strategy is applied to create mesh density distribution map which is afterwards used by the mesh generator to produce the next, appropriately (de)refined mesh. The new mesh is subjected to a new partitioning and passed again to the finite element solver which is restarted from the previous step, when the relative error was still below the defined threshold. The solution (primary unknowns as well as the state variables) from this step is mapped on the new mesh, the equilibrium and consistency are recovered and the analysis continues as long as the error remains within the permissible range. This process is repeated until the analysis is completed.

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.

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Daniel Rypl