Multigrid solver with automatic mesh refinement for transient elastoplastic dynamic problems

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.

[1]  David Dureisseix,et al.  Information transfer between incompatible finite element meshes: Application to coupled thermo-viscoelasticity , 2006 .

[2]  Alain Combescure,et al.  Multi‐time‐step and two‐scale domain decomposition method for non‐linear structural dynamics , 2003 .

[3]  J. Hall,et al.  The multigrid method in solid mechanics: Part I—Algorithm description and behaviour , 1990 .

[4]  Jacob Fish,et al.  An efficient multilevel solution scheme for large scale non-linear systems , 1995 .

[5]  Nathan M. Newmark,et al.  A Method of Computation for Structural Dynamics , 1959 .

[6]  Alain Combescure,et al.  Automatic energy conserving space–time refinement for linear dynamic structural problems , 2005 .

[7]  Alain Combescure,et al.  Efficient FEM calculation with predefined precision through automatic grid refinement , 2005 .

[8]  Robert L. Taylor,et al.  Parallel multigrid solvers for 3D-unstructured large deformation elasticity and plasticity finite element problems , 2000 .

[9]  I. Babuska,et al.  A‐posteriori error estimates for the finite element method , 1978 .

[10]  Josep Sarrate,et al.  Adaptive finite element strategies based on error assessment , 1999 .

[11]  Nils-Erik Wiberg,et al.  Adaptive multigrid for finite element computations in plasticity , 2004 .

[12]  Shripad Thite,et al.  An h-adaptive spacetime-discontinuous Galerkin method for linear elastodynamics , 2006 .

[13]  D. Mavriplis.  An assessment of linear versus non-linear multigrid methods for unstructured mesh solvers , 2001 .

[14]  Folco Casadei,et al.  Binary spatial partitioning of the central‐difference time integration scheme for explicit fast transient dynamics , 2009 .

[15]  I. D. Parsons,et al.  A parallel multigrid method for history-dependent elastoplasticity computations , 1993 .

[16]  D. Brandt,et al.  Multi-level adaptive solutions to boundary-value problems math comptr , 1977 .

[17]  J. Z. Zhu,et al.  The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique , 1992 .

[18]  A. Combescure,et al.  Coupling subdomains with heterogeneous time integrators and incompatible time steps , 2009 .

[19]  Shripad Thite.  Adaptive spacetime meshing for discontinuous Galerkin methods , 2009, Comput. Geom..