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Portero Egea, Laura

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https://academica-e.unavarra.es/handle/2454/49803

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Portero Egea

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Laura

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Estadística, Informática y Matemáticas

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InaMat2. Instituto de Investigación en Materiales Avanzados y Matemáticas

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0000-0002-7521-2097

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2608

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2004 - 20073
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Now showing 1 - 3 of 3
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    PublicationOpen Access
    Parallel solution of nonlinear parabolic problems on logically rectangular grids
    (Springer, 2007) Arrarás Ventura, Andrés; Portero Egea, Laura; Jorge Ulecia, Juan Carlos; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
    This work deals with the efficient numerical solution of nonlinear transient flow problems posed on two-dimensional porous media of general geometry. We first consider a spatial semidiscretization of such problems by using a cell-centered finite difference scheme on a logically rectangular grid. The resulting nonlinear stiff initial-value problems are then integrated in time by means of a fractional step method, combined with a decomposition of the flow domain into a set of overlapping subdomains and a linearization procedure which involves suitable Taylor expansions. The proposed algorithm reduces the original problem to the solution of several linear systems per time step. Moreover, each one of such systems can be directly decomposed into a set of uncoupled linear subsystems which can be solved in parallel. A numerical example illustrates the unconditionally convergent behaviour of the method in the last section of the paper.
  • Thumbnail Image
    PublicationOpen Access
    A combined fractional step domain decomposition method for the numerical integration of parabolic problems
    (Springer, 2004) Portero Egea, Laura; Bujanda Cirauqui, Blanca; Jorge Ulecia, Juan Carlos; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
    In this paper we develop parallel numerical algorithms to solve linear time dependent coefficient parabolic problems. Such methods are obtained by means of two consecutive discretization procedures. Firstly, we realize a time integration of the original problem using a Fractional Step Runge Kutta method which provides a family of elliptic boundary value problems on certain subdomains of the original domain. Next, we discretize those elliptic problems by means of standard techniques. Using this framework, the numerical solution is obtained by solving, at each stage, a set of uncoupled linear systems of low dimension. Comparing these algorithms with the classical domain decomposition methods for parabolic problems, we obtain a reduction of computational cost because of, in this case, no Schwarz iterations are required. We give an unconditional convergence result for the totally discrete scheme and we include two numerical examples that show the behaviour of the proposed method.
  • Thumbnail Image
    PublicationOpen Access
    Embedded pairs of fractional step Runge-Kutta methods and improved domain decomposition techniques for parabolic problems
    (Springer, 2007) Portero Egea, Laura; Jorge Ulecia, Juan Carlos; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
    In this paper we design and apply new embedded pairs of Frac- tional Step Runge-Kutta methods to the e±cient solution of multidimensional parabolic problems. These time integrators are combined with a suitable split- ting of the elliptic operator subordinated to a decomposition of the spatial domain and a standard spatial discretization. With this technique we ob- tain parallel algorithms which have the main advantages of classical domain decomposition methods and, besides, avoid iterative processes like Schwarz iterations, typical of them. The use of these embedded methods permits a fast variable step time integration process.