Thirty years of the finite volume method for solid mechanics

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. Proche 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…

2. Apparenté Pas pertinent

   On the implementation of the eXtended Finite Element Method (XFEM) for interface problems

   Thomas Carraro, Sven Wetterauer · 2015 · Analyse numérique · Résumé IA disponible

   Résumé scientifique

   The eXtended Finite Element Method (XFEM) is used to solve interface problems with an unfitted mesh. We present an implementation of the XFEM in the FEM-library deal.II. The main parts of the implementation are (i) the appropriate quadrature rule; (ii) the shape functions for the extended part of the finite element formulation; (iii) the boundary and interface conditions. We show how to handle the XFEM formulation providing a code that demonstrates the solution of two exemplary interface problems for a strong and a weak discontinuity respectively. In the weak discontinuity case, the loss of conformity due to the blending effect and its remedy are discussed. Furthermore, the optimal convergen…

3. 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…

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

   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…

6. Apparenté Pas pertinent

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

   Dean Muir, Kenneth Duru, Matthew Hole et al. · 2023 · Analyse numérique · Résumé IA disponible

   Résumé scientifique

   We present a novel numerical method for solving the anisotropic diffusion equation in toroidally confined magnetic fields which is efficient, accurate and provably stable. The continuous problem is written in terms of a derivative operator for the perpendicular transport and a linear operator, obtained through field line tracing, for the parallel transport. We derive energy estimates of the solution of the continuous initial boundary value problem. A discrete formulation is presented using operator splitting in time with the summation by parts finite difference approximation of spatial derivatives for the perpendicular diffusion operator. Weak penalty procedures are derived for implementing …

7. 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…

8. Apparenté Pas pertinent

   Gradual Variation Analysis for Groundwater Flow

   Li Chen · 2010 · Analyse numérique · Pas encore résumé

   Résumé scientifique

   Groundwater flow in Washington DC greatly influences the surface water quality in urban areas. The current methods of flow estimation, based on Darcy's Law and the groundwater flow equation, can be described by the diffusion equation (the transient flow) and the Laplace equation (the steady-state flow). The Laplace equation is a simplification of the diffusion equation under the condition that the aquifer has a recharging boundary. The practical way of calculation is to use numerical methods to solve these equations. The most popular system is called MODFLOW, which was developed by USGS. MODFLOW is based on the finite-difference method in rectangular Cartesian coordinates. MODFLOW can be vie…