Um Framework para Análise Seqüencial e em Paralelo de Sólidos Elásticos pelo Método dos Elementos Finitos

AUTOR(ES)

Bianca de Almeida Dantas

DATA DE PUBLICAÇÃO

2006

RESUMO

The objective of this work is the development of a C++ framework for finite element method (FEM) that provides sequential and parallel analysis of elastic solids. FEM is based on the discretization of the domain analyzed into a mesh, resulting on the transformation of the diferential equations that define elasticity into a linear equations system which for tridimensional problems may contain thousands of equations. Since obtaining and solving those systems are computation intensive tasks, it makes sense searching for alternatives that make FEM analysis more eficient, emphasizing parallel computing. Parallel analysis is performed through p processors, each one responsible for analyzing a part of the domain. In order to make it possible, the solid is split into p parts or subdomains. Each part is sent to a diferent processor and separately analyzed. In this phase the boundary points among subdomains are considered fixed. After each subdomain is analyzed in parallel, the global analysis results in the boundary nodes can be calculated using a substructuring technique. Internal results in each subdomain can then be obtained in parallel with the boundary nodes results. Among diferent possible alternatives for domain decomposition, we chose to use a technique based on partitioning the graph whose vertexes are equivalent to the mesh elements and edges connect vertexes which represent adjacent elements of the mesh. METIS package was chosen as the partitioning graphs tool, aiming that its component functions were encapsulated in a C++ class and attached to the framework. In order to send objects through diferent processors during analysis, one implemented a serialization scheme which transforms an object into a contiguous byte flow and, inversely, obtains the original object which originated a byte flow. MPI (message passing interface) communication library was used to grant sending and receiving byte flows.

ASSUNTO(S)

método de elementos finitos parallel computing programação orientada a objetos computational mechanics ciencia da computacao finite element method mecânica computacional domain decomposition object-oriented programming decomposição de domínio computação paralela

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