Automatic Local Error Control for 3D Non Linear Transient Dynamics with Multigrid Finite Elements

Abstract eng:
It is of great interest for safety issues as well as for quality of the simulation to evaluate the quality and the precision of a numerical simulation: for example, one would like to control of maximum plastic strain in any point of the structure or the kinetic energy everywhere, or any other local quantity of interest. This problem is well known and has been studied from a long time for example with adaptative techniques in quasitatic linear or non linear analysis. The applications in dynamics are scarcer [1] and the applications for elastoplastic transient computations are rare [2]. This paper is dedicated to the presentation of a method based on localised multigrid to control the quality of the local quantity of a nonlinear transient computation within a unique run. The method provides the transient elastoplastic solution which verifies the requested precision anywhere and at any time. The basic idea is to refine locally at each time step a basic coarse mesh recursively until the requested precision on the quantity of interest is obtained. The reverse coarsening operation is also activated when the results are too “good”. The method will be explained and illustrated on 2D examples as well as on 3D cases for which the converged solution implies so fine meshes in some part that the 3D computation using this mesh size everywhere is impossible (not enough memory….) or extremely CPU time consuming. Moreover one shall observe that due to transient nature of the solution the finer meshed zones are moving with time.

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