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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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2007 - 200912010 - 20182
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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.
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    PublicationOpen Access
    Improved accuracy for time-splitting methods for the numerical solution of parabolic equations
    (Elsevier, 2015) Arrarás Ventura, Andrés; Portero Egea, Laura; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
    In this work, we study time-splitting strategies for the numerical approximation of evolutionary reaction–diffusion problems. In particular, we formulate a family of domain decomposition splitting methods that overcomes some typical limitations of classical alternating direction implicit (ADI) schemes. The splitting error associated with such methods is observed to be O(t2) in the time step. In order to decrease the size of this splitting error to O(t3), we add a correction term to the right-hand side of the original formulation. This procedure is based on the improved initialization technique proposed by Douglas and Kim in the framework of ADI methods. The resulting non-iterative schemes reduce the global system to a collection of uncoupled subdomain problems that can be solved in parallel. Computational results comparing the newly derived algorithms with the Crank–Nicolson scheme and certain ADI methods are presented.
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    PublicationOpen Access
    Decoupling mixed finite elements on hierarchical triangular grids for parabolic problems
    (Elsevier, 2018) Arrarás Ventura, Andrés; Portero Egea, Laura; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
    In this paper, we propose a numerical method for the solution of time-dependent flow problems in mixed form. Such problems can be efficiently approximated on hierarchical grids, obtained from an unstructured coarse triangulation by using a regular refinement process inside each of the initial coarse elements. If these elements are considered as subdomains, we can formulate a non-overlapping domain decomposition method based on the lowest-order Raviart–Thomas elements, properly enhanced with Lagrange multipliers on the boundaries of each subdomain (excluding the Dirichlet edges). A suitable choice of mixed finite element spaces and quadrature rules yields a cell-centered scheme for the pressures with a local 10-point stencil. The resulting system of differential-algebraic equations is integrated in time by the Crank–Nicolson method, which is known to be a stiffly accurate scheme. As a result, we obtain independent subdomain linear systems that can be solved in parallel. The behavior of the algorithm is illustrated on a variety of numerical experiments.