Adaptatividade hp em paralelo / Hp adaptive technique in parallel

Edimar Cesar Rylo

This work presents a study of hp adaptive methods applied to finite element approximations. Two topics are emphasized: analysis of the quality of the approximation and methodology of refinement of the approximation space. The main objective of the work is to conceive a framework for developing hp-adaptive algorithms within the PZ environment. The framework is independent of the weak statement, type of element or resolution method. The framework uses separate interfaces to define the error estimation method and selection of refinement pattern. Secondly, the framework was ported to parallel processing using the object oriented framework OOPar. The intent of parallelizing the adaptive process is to reduce the time spent in error estimation and choice of the optimal refinement pattern and thus bring adaptivity to a level where it can be used as a routine analysis method. Both error estimation and choice of refinement pattern are implemented on a shared and/or distributed machine. Finally, a methodology was developed to extend the h-adaptive refinement process based on refinement patterns. Together with the implementation of refinement patterns, a procedure was developed to check on the compatibility of refinement patterns of two neighboring elements. The choice of the "best" refinement patterns is one of the main challenges of adaptive methods (Zienkiewicz [55]). The availability of different ways of refining elements increases the flexibility of the code, but also introduces the challenge of deciding which pattern is the "best" pattern. It is possible that the combination of optimized h-refinement together with choice of h and/or p refinement may lead to very efficient approximation spaces for a given problem

Adaptatividade hp em paralelo / Hp adaptive technique in parallel

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