Person: Portero Egea, Laura
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Portero Egea
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Laura
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Estadística, Informática y Matemáticas
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0000-0002-7521-2097
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2608
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Publication Open Access Geometric multigrid methods for Darcy–Forchheimer flow in fractured porous media(Elsevier, 2019) Arrarás Ventura, Andrés; Gaspar, F. J.; Portero Egea, Laura; Rodrigo, C.; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaIn this paper, we present a monolithic multigrid method for the efficient solution of flow problems in fractured porous media. Specifically, we consider a mixed-dimensional model which couples Darcy flow in the porous matrix with Forchheimer flow within the fractures. A suitable finite volume discretization permits to reduce the coupled problem to a system of nonlinear equations with a saddle point structure. In order to solve this system, we propose a full approximation scheme (FAS) multigrid solver that appropriately deals with the mixed-dimensional nature of the problem by using mixed-dimensional smoothing and inter-grid transfer operators. Numerical experiments show that the proposed multigrid method is robust with respect to the fracture permeability, the Forchheimer coefficient and the mesh size. The case of several possibly intersecting fractures in a heterogeneous porous medium is also discussed.Publication Open Access Mixed-dimensional geometric multigrid methods for single-phase flow in fractured porous media(SIAM, 2019) Arrarás Ventura, Andrés; Gaspar, F. J.; Portero Egea, Laura; Rodrigo, C.; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaThis paper deals with the efficient numerical solution of single-phase flow problems in fractured porous media. A monolithic multigrid method is proposed for solving two-dimensional arbitrary fracture networks with vertical and/or horizontal possibly intersecting fractures. The key point is to combine two-dimensional multigrid components (smoother and intergrid transfer operators) in the porous matrix with their one-dimensional counterparts within the fractures, giving rise to a mixed-dimensional geometric multigrid method. This combination seems to be optimal since it provides an algorithm whose convergence matches the multigrid convergence factor for solving the Darcy problem. Several numerical experiments are presented to demonstrate the robustness of the monolithic mixed-dimensional multigrid method with respect to the permeability of the fractures, the grid size, and the number of fractures in the network.Publication Open Access Multipoint flux mixed finite element methods for slightly compressible flow in porous media(Elsevier, 2019) Arrarás Ventura, Andrés; Portero Egea, Laura; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaIn this paper, we consider multipoint flux mixed finite element discretizations for slightly compressible Darcy flow in porous media. The methods are formulated on general meshes composed of triangles, quadrilaterals, tetrahedra or hexahedra. An inexact Newton method that allows for local velocity elimination is proposed for the solution of the nonlinear fully discrete scheme. We derive optimal error estimates for both the scalar and vector unknowns in the semidiscrete formulation. Numerical examples illustrate the convergence behavior of the methods, and their performance on test problems including permeability coefficients with increasing heterogeneity.Publication Open 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 IngeniaritzaIn 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.Publication Open 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 IngeniaritzaIn 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.Publication Open Access Modified Douglas splitting methods for reaction–diffusion equations(Springer, 2017) Arrarás Ventura, Andrés; Hout, K. J. in ’t; Hundsdorfer, W.; Portero Egea, Laura; Ingeniería Matemática e Informática; Matematika eta Informatika IngeniaritzaWe present modifications of the second-order Douglas stabilizing corrections method, which is a splitting method based on the implicit trapezoidal rule. Inclusion of an explicit term in a forward Euler way is straightforward, but this will lower the order of convergence. In the modifications considered here, explicit terms are included in a second-order fashion. For these modified methods, results on linear stability and convergence are derived. Stability holds for important classes of reaction–diffusion equations, and for such problems the modified Douglas methods are seen to be often more efficient than related methods from the literature.