Parallel complete remeshing for adaptive schemes

Abstract

In order to improve the convergence ratio and to automate Finite Element Methods, several strategies have been introduced. One of these is the adaptive scheme. This approximation presents limitations for parallelism since the generation of a conformal, valid and well conditioned finite element mesh is a time consuming task, and now it appears as a main task in each iteration of the adaptation procedure. This work is motivated by the use of the h-adaptive method in its most flexible form, where a complete reconstruction of the whole mesh have to be performed whenever a solution over the current mesh has been obtained and until error criteria are achieved. We focused on the problem of the fast generation of tetrahedral unstructured meshes in a parallel fashion over geometric models with some given refinement criteria. The chosen strategy implies the use of an octal tree, octree, as a key hierarchical data structure to guide the algorithm. The codes have been developed using the MPI library in a SGI Origin 200 multiprocessor.