Provably stable numerical method for the anisotropic diffusion equation in toroidally confined magnetic fields

Classés selon la proximité de leur titre et de leur résumé avec ceux de cet article. Sélectionnez-en pour les lire ensemble.

Les articles les plus proches

1. Apparenté Pas pertinent

   An embedded corrector problem for homogenization. Part II: Algorithms and discretization

   Eric Cancès, Virginie Ehrlacher, Frederic Legoll et al. · 2018 · Analyse numérique · Pas encore résumé

   Résumé scientifique

   This contribution is the numerically oriented companion article of the work [E. Canc\`es, V. Ehrlacher, F. Legoll, B. Stamm and S. Xiang, arxiv preprint 1807.05131]. We focus here on the numerical resolution of the embedded corrector problem introduced in [E. Canc\`es, V. Ehrlacher, F. Legoll and B. Stamm, CRAS 2015; E. Canc\`es, V. Ehrlacher, F. Legoll, B. Stamm and S. Xiang, arxiv preprint 1807.05131] in the context of homogenization of diffusion equations. Our approach consists in considering a corrector-type problem, posed on the whole space, but with a diffusion matrix which is constant outside some bounded domain. In [E. Canc\`es, V. Ehrlacher, F. Legoll, B. Stamm and S. Xiang, arxiv p…

2. Apparenté Pas pertinent

   A robust solution strategy for the Cahn-Larché equations

   Erlend Storvik, Jakub Wiktor Both, Jan Martin Nordbotten et al. · 2022 · Analyse numérique · Résumé IA disponible

   Résumé scientifique

   In this paper we propose a solution strategy for the Cahn-Larch\'e equations, which is a model for linearized elasticity in a medium with two elastic phases that evolve subject to a Ginzburg-Landau type energy functional. The system can be seen as a combination of the Cahn-Hilliard regularized interface equation and linearized elasticity, and is non-linearly coupled, has a fourth order term that comes from the Cahn-Hilliard subsystem, and is non-convex and nonlinear in both the phase-field and displacement variables. We propose a novel semi-implicit discretization in time that uses a standard convex-concave splitting method of the nonlinear double-well potential, as well as special treatment…

3. Apparenté Pas pertinent

   Compatible finite element methods for geophysical fluid dynamics

   Colin J. Cotter · 2023 · Analyse numérique · Résumé IA disponible

   Résumé scientifique

   This article surveys research on the application of compatible finite element methods to large scale atmosphere and ocean simulation. Compatible finite element methods extend Arakawa's C-grid finite difference scheme to the finite element world. They are constructed from a discrete de Rham complex, which is a sequence of finite element spaces which are linked by the operators of differential calculus. The use of discrete de Rham complexes to solve partial differential equations is well established, but in this article we focus on the specifics of dynamical cores for simulating weather, oceans and climate. The most important consequence of the discrete de Rham complex is the Hodge-Helmholtz d…

4. Apparenté Pas pertinent

   A Computationally Efficient Vectorized Implementation of Localizing Gradient Damage Method in MATLAB

   Subrato Sarkar · 2023 · Analyse numérique · Résumé IA disponible

   Résumé scientifique

   In this work, a recently developed fracture modeling method called localizing gradient damage method (LGDM) is implemented in MATLAB. MATLAB is well-known in the computational research community for its simple and easy-to-learn coding interface. As a result, MATLAB is generally preferred for the initial development (prototyping) of computational models by researchers. However, MATLAB-developed codes are seldom used for large-scale simulations (after initial development is complete) due to their computational inefficiency. Hence, a computationally efficient implementation of LGDM using MATLAB vectorization is presented in this work. The choice of LGDM (as the fracture modeling method) is base…

5. Apparenté Pas pertinent

   An overview on deep learning-based approximation methods for partial differential equations

   Christian Beck, Martin Hutzenthaler, Arnulf Jentzen et al. · 2020 · Discrete Contin. Dyn. Syst. Ser. B 28 (2023), no. 6, 3697-3746 · Résumé IA disponible

   Résumé scientifique

   It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). Recently, several deep learning-based approximation algorithms for attacking this problem have been proposed and tested numerically on a number of examples of high-dimensional PDEs. This has given rise to a lively field of research in which deep learning-based methods and related Monte Carlo methods are applied to the approximation of high-dimensional PDEs. In this article we offer an introduction to this field of research by revisiting selected mathematical results related to deep learning approximation methods for PDEs and reviewing the main ide…

6. Apparenté Pas pertinent

   A robust monolithic solver for phase-field fracture integrated with fracture energy based arc-length method and under-relaxation

   Ritukesh Bharali, Somdatta Goswami, Cosmin Anitescu et al. · 2021 · Analyse numérique · Résumé IA disponible

   Résumé scientifique

   The phase-field fracture free-energy functional is non-convex with respect to the displacement and the phase field. This results in a poor performance of the conventional monolithic solvers like the Newton-Raphson method. In order to circumvent this issue, researchers opt for the alternate minimization (staggered) solvers. Staggered solvers are robust for the phase-field based fracture simulations as the displacement and the phase-field sub-problems are convex in nature. Nevertheless, the staggered solver requires very large number of iterations (of the order of thousands) to converge. In this work, a robust monolithic solver is presented for the phase-field fracture problem. The solver adop…

7. Apparenté Pas pertinent

   Thirty years of the finite volume method for solid mechanics

   Philip Cardiff, Ismet Demirdžić · 2018 · Analyse numérique · Résumé IA disponible

   Résumé scientifique

   Since early publications in the late 1980s and early 1990s, the finite volume method has been shown suitable for solid mechanics analyses. At present, there are several flavours of the method, which can be classified in a variety of ways, such as grid arrangement (cell-centred vs staggered vs vertex-centred), solution algorithm (implicit vs explicit), and stabilisation strategy (Rhie-Chow vs Jameson-Schmidt-Turkel vs Godunov upwinding). This article gives an overview, historical perspective, comparison and critical analysis of the different approaches where a close comparison with the de facto standard for computational solid mechanics, the finite element method, is given. The article finish…

8. Apparenté Pas pertinent

   Convergence of an adaptive $C^0$-interior penalty Galerkin method for the biharmonic problem

   Alexander Dominicus, Fernando Gaspoz, Christian Kreuzer · 2019 · Analyse numérique · Résumé IA disponible

   Résumé scientifique

   We develop a basic convergence analysis for an adaptive $\textsf{C}^0\textsf{IPG}$ method for the Biharmonic problem, which provides convergence without rates for all practically relevant marking strategies and all penalty parameters assuring coercivity of the method. The analysis hinges on embedding properties of (broken) Sobolev and BV spaces, and the construction of a suitable limit space. In contrast to the convergence result of adaptive discontinuous Galerkin methods for elliptic PDEs, by Kreuzer and Georgoulis [Math. Comp. 87 (2018), no.~314, 2611--2640], here we have to deal with the fact that the Lagrange finite element spaces may possibly contain no proper $C^1$-conforming subspace.…