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Multigrid solver with automatic mesh refinement for transient elastoplastic dynamic problems
Author(s) -
Biotteau E.,
Gravouil A.,
Lubrecht A. A.,
Combescure A.
Publication year - 2010
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2927
Subject(s) - multigrid method , polygon mesh , solver , adaptive mesh refinement , computer science , finite element method , transient (computer programming) , algorithm , subdivision , mathematical optimization , computational science , mesh generation , scheme (mathematics) , mathematics , partial differential equation , structural engineering , computer graphics (images) , engineering , mathematical analysis , civil engineering , operating system
Abstract This paper presents an adaptive refinement strategy based on a hierarchical element subdivision dedicated to modelling elastoplastic materials in transient dynamics. At each time step, the refinement is automatic and starts with the calculation of the solution on a coarse mesh. Then, an error indicator is used to control the accuracy of the solution and a finer localized mesh is created where the user‐prescribed accuracy is not reached. A new calculation is performed on this new mesh using the non‐linear ‘Full Approximation Scheme’ multigrid strategy. Applying the error indicator and the refinement strategy recursively, the optimal mesh is obtained. This mesh verifies the error indicator on the whole structure. The multigrid strategy is used for two purposes. First, it optimizes the computational cost of the solution on the finest localized mesh. Second, it ensures information transfer among the different hierarchical meshes. A standard time integration scheme is used and the mesh is reassessed at each time step. Copyright © 2010 John Wiley & Sons, Ltd.