Multigrid solver with automatic mesh refinement for transient elastoplastic dynamic problems

Abstract

International audienceThis paper presents an adaptive refinement strategy based on a hierarchical element subdivision dedicated to modeling 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'' (FAS) 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 amongst the different hierarchical meshes. A standard time integration scheme is used and the mesh is reassessed at each time step

Three dimensional automatic refinement method for transient small strain elastoplastic finite element computations

“…Nevertheless, this correlation as been confirmed for one-dimensional examples [5] and two-dimensional examples [6] and is expected to be the same for three-dimensional problems.…”

“…This paper extends the non-linear adaptive multigrid algorithm dedicated to transient non-linear dynamics problems presented in [6] to three-dimensional simulations and gives extra information on the error indicators.…”

“…Moreover, the multigrid process accelerates the convergence rate such that the gain in computing time is even higher. For a two-dimensional problem the element saving is about 1 for 15 and induces a gain in calculation time of about 40 [6]. For three dimensional problems, the CPU time saving is expected to be greater as the number of nodes and Gauss points is higher.…”

Volumetric coupling approaches for multiphysics simulations on non‐matching meshes

“…In contrast, the second approach is based VOLUMETRIC COUPLING FOR MULTIPHYSICS ON NON-MATCHING MESHES 1551 on the mortar method [5][6][7][8] and enforces the information transfer in an integral sense. Nodal information transfer is also required for classical remeshing procedures [9][10][11], geometrical multigrid methods [12,13], and zooming techniques like the Arlequin method for structural problems [14,15] and the Chimera scheme for fluid problems [16,17].…”

Strategies involving the local defect correction multi-level refinement method for solving three-dimensional linear elastic problems

“…To automate the refinement process, these methods are therefore often combined with a posteriori error estimators (e.g. [7,3,16,22,34,35]).…”