Doutorado em Ciência da Computação

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http://repositorio.ufes.br/handle/10/17626

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Navegando Doutorado em Ciência da Computação por Autor "Almeida, Regina Célia Cerqueira de"

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    An alternative approach of parallel preconditioning for 2D finite element problems
    (Universidade Federal do Espírito Santo, 2018-06-29) Lima, Leonardo Muniz de; Catabriga, Lucia; Almeida, Regina Célia Cerqueira de; Santos, Isaac Pinheiro dos; Souza, Alberto Ferreira de; Elias, Renato Nascimento
    We propose an alternative approach of parallel preconditioning for 2D finite element problems. This technique consists in a proper domain decomposition with reordering that produces narrowband linear systems from finite element discretization, allowing to apply, without significant efforts, traditional preconditioners as Incomplete LU Factorization (ILU) or even sophisticated parallel preconditioners as SPIKE. Another feature of that approach is the facility to recalculate finite element matrices whether for nonlinear corrections or for time integration schemes. That means parallel finite element application is performed indeed in parallel, not just to solve the linear system. We also employ preconditioners based on element-by-element storage with minimal adjustments. Robustness and scalability of these parallel preconditioning strategies are demonstrated for a set of benchmark experiments. We consider a group of two-dimensional fluid flow problems modeled by transport, and Euler equations to evaluate ILU, SPIKE, and some element-by-element preconditioners. Moreover, our approach provides load balancing and improvement to MPI communications. We study the load balancing and MPI communications through analyzer tools as TAU (Tuning Analysis Utilities).
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    Nonlinear multiscale viscosity methods and time integration schemes for solving compressible Euler equations
    (Universidade Federal do Espírito Santo, 2018-06-29) Bento, Sérgio Souza; Santos, Isaac Pinheiro dos; Catabriga, Lucia; Almeida, Regina Célia Cerqueira de; Malta, Sandra Mara Cardoso; Boeres, Maria Claudia Silva; Valli, Andrea Maria Pedrosa
    In this work we present nonlinear multiscale finite element methods for solving compressible Euler equations. The formulations are based on the strategy of separating scales – the core of the variational multiscale (finite element) methodology. The subgrid scale space is defined using bubble functions that vanish on the boundary of the elements, allowing to use a local Schur complement to define the resolved scale problem. The resulting numerical procedure allows the fine scales to depend on time. The formulations proposed in this work are residual based considering different ways for the artificial viscosity to act on all scales of the discretization. In the first formulation a nonlinear operator is added on all scales whereas in the second different nonlinear operators are included on macro and micro scales. We evaluate the efficiency of the formulations through numerical studies, comparing them with the SUPG combined with the shock-capturing operator YZβ and the CAU methodologies. Another contribution of this work concerns the time integration procedure. Density-based schemes suffer with undesirable effects of low speed flow including low convergence rate and loss of accuracy. Due to this phenomenon, local preconditioning is applied to the set of equations in the continuous case. Another alternative to solve this deficiency consists of using time integration methods with a stiff decay property. For this purpose, we propose a predictor-corrector method based on Backward Differentiation Formulas (BDF) that is not defined in the traditional sense found in the literature, i.e., using a predictor based on extrapolation.