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Pré-condicionador multiescala algébrico aplicado à simulação de reservatórios de petróleo

  • Magri, Victor Antonio Paludetto
Publication Date
Jan 01, 2015
Repositório Institucional da UFSC
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Abstract : One of the major challenges faced by reservoir simulation is about the solution of the linear systems obtained by the discretization of elliptic equations. This task turns out to be even more complex when highly heterogeneous permeability fields are present. Different strategies of direct and iterative methods have been developed in the last years and employed in this context. Considering the last ones, it s possible to note that iterative methods built by multigrid preconditioners are the most employed because of their robustness and efficiency. In this work, the mathematical properties and the computational performance of multigrid-like preconditioners called multiscale preconditioners are evaluated. The studied alternatives are implemented computationally and employed in conjunction of iterative methods for the precise and approximate solution of challenging elliptic problems. Given the tested problems, it was possible to verify that the best configuration properties for a multiscale preconditioner are composed by a galerkin restriction operator, smoothers based on incomplete factorization and coarsening ratios around of ten for each direction of the grid. Several others solutions strategies available in the scientific package PETSc were evaluated using the same set of problems as before and it was possible to conclude that the BoomerAMG preconditioner associated with the conjugate gradient method as well as the direct method Cholesky-UMFPACK are the most efficient ones in both mathematical and computational evaluation points and are even better than the multiscale preconditioner when the intention is to get a precise solution.

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