| 1. |
- Berre, I., et al.
(författare)
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Verification benchmarks for single-phase flow in three-dimensional fractured porous media
- 2021
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Ingår i: Advances in Water Resources. - OXFORD ENGLAND : Elsevier BV. - 0309-1708 .- 1872-9657. ; 147
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Tidskriftsartikel (refereegranskat)abstract
- Flow in fractured porous media occurs in the earth's subsurface, in biological tissues, and in man-made materials. Fractures have a dominating influence on flow processes, and the last decade has seen an extensive development of models and numerical methods that explicitly account for their presence. To support these developments, four benchmark cases for single-phase flow in three-dimensional fractured porous media are presented. The cases are specifically designed to test the methods’ capabilities in handling various complexities common to the geometrical structures of fracture networks. Based on an open call for participation, results obtained with 17 numerical methods were collected. This paper presents the underlying mathematical model, an overview of the features of the participating numerical methods, and their performance in solving the benchmark cases.
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| 2. |
- Boon, Wietse M., et al.
(författare)
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An Adaptive Penalty Method for Inequality Constrained Minimization Problems
- 2021
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Ingår i: European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019. - Cham : Springer Science and Business Media Deutschland GmbH. ; , s. 155-164
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Konferensbidrag (refereegranskat)abstract
- The primal-dual active set method is observed to be the limit of a sequence of penalty formulations. Using this perspective, we propose a penalty method that adaptively becomes the active set method as the residual of the iterate decreases. The adaptive penalty method (APM) therewith combines the main advantages of both methods, namely the ease of implementation of penalty methods and the exact imposition of inequality constraints inherent to the active set method. The scheme can be considered a quasi-Newton method in which the Jacobian is approximated using a penalty parameter. This spatially varying parameter is chosen at each iteration by solving an auxiliary problem.
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| 3. |
- Boon, Wietse M., et al.
(författare)
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Stable mixed finite elements for linear elasticity with thin inclusions
- 2021
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Ingår i: Computational Geosciences. - : Springer Nature. - 1420-0597 .- 1573-1499. ; 25:2, s. 603-620
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Tidskriftsartikel (refereegranskat)abstract
- We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of hierarchically connected manifolds is formed which we refer to as mixed-dimensional. The governing equations with respect to linear elasticity are then defined on this mixed-dimensional geometry. The resulting system of partial differential equations is also referred to as mixed-dimensional, since functions defined on domains of multiple dimensionalities are considered in a fully coupled manner. With the use of a semi-discrete differential operator, we obtain the variational formulation of this system in terms of both displacements and stresses. The system is then analyzed and shown to be well-posed with respect to appropriately weighted norms. Numerical discretization schemes are proposed using well-known mixed finite elements in all dimensions. The schemes conserve linear momentum locally while relaxing the symmetry condition on the stress tensor. Stability and convergence are shown using a priori error estimates and confirmed numerically.
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| 4. |
- Boon, Wietse M., et al.
(författare)
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Robust preconditioners for perturbed saddle-point problems and conservative discretizations of Biot's equations utilizing total pressure
- 2021
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Ingår i: SIAM Journal on Scientific Computing. - : Society for Industrial & Applied Mathematics (SIAM). - 1064-8275 .- 1095-7197. ; 43:4, s. B961-B983
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Tidskriftsartikel (refereegranskat)abstract
- We develop robust solvers for a class of perturbed saddle-point problems arising in the study of a second-order elliptic equation in mixed form (in terms of flux and potential), and of the four-field formulation of Biot's consolidation problem for linear poroelasticity (using displacement, filtration flux, total pressure, and fluid pressure). The stability of the continuous variational mixed problems, which hinges upon using adequately weighted spaces, is addressed in detail; and the efficacy of the proposed preconditioners, as well as their robustness with respect to relevant material properties, is demonstrated through several numerical experiments.
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