Multimesh finite element methods: Solving PDEs on multiple intersecting meshes

被引:29
作者
Johansson, August [1 ,2 ]
Kehlet, Benjamin [2 ]
Larson, Mats G. [3 ]
Logg, Anders [4 ,5 ]
机构
[1] SINTFF Digital, Math & Cybernet, POB 124 Blindern, N-0314 Oslo, Norway
[2] Simula Res Lab, POB 134, N-1325 Lysaker, Norway
[3] Umea Univ, Dept Math & Math Stat, S-90187 Umea, Sweden
[4] Chalmers Univ Technol, Dept Math Sci, S-41296 Gothenburg, Sweden
[5] Univ Gothenburg, S-41296 Gothenburg, Sweden
基金
瑞典研究理事会;
关键词
FEM; Unfitted mesh; Non-matching mesh; Multimesh; CutFEM; Nitsche; SOLID MECHANICS; NITSCHES METHOD; CELL METHOD; DISCONTINUOUS GALERKIN; DOMAIN DECOMPOSITION; OVERLAPPING GRIDS; INTEGRATION; REFINEMENT; ELASTICITY; BOUNDARY;
D O I
10.1016/j.cma.2018.09.009
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are naturally separate; such as the components of an engine, the domains of a multiphysics problem, or solid bodies interacting under the influence of forces from surrounding fluids or other physical fields. Such multimesh finite element methods are particularly well suited to problems in which the computational domain undergoes large deformations as a result of the relative motion of the separate components of a multi-body system. In the present paper, we formulate the multimesh finite element method for the Poisson equation. Numerical examples demonstrate the optimal order convergence, the numerical robustness of the formulation and implementation in the face of thin intersections and rounding errors, as well as the applicability of the methodology. In the accompanying paper (Johansson et al., 2018), we analyze the proposed method and prove optimal order convergence and stability. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码:672 / 689
页数:18
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