首页|Space-time adaptive splitting scheme for the numerical simulation of polycrystallization
Space-time adaptive splitting scheme for the numerical simulation of polycrystallization
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NSTL
Elsevier
We consider a space-time adaptive splitting scheme for polycrystallization processes described by a two-field phase field model. The phase field model consists of a coupled system of evolutionary processes for the local degree of crystallinity phi and the orientation angle Theta one of them being of first order total variation flow type. The splitting scheme is based on an implicit discretization in time which allows a decoupling of the system in the sense that at each time step minimization problems in phi and Theta have to be solved successively. The discretization in space is taken care of by a standard finite element approximation for the problem in phi and an Interior Penalty Discontinuous Galerkin (IPDG) approximation for the one in Theta. The adaptivity in space relies on equilibrated a posteriori error estimators for the discretization errors in phi and Theta in terms of primal and dual energy functionals associated with the respective minimization problems. The adaptive time stepping is dictated by the convergence of a semismooth Newton method for the numerical solution of the nonlinear problem in Theta. Numerical results illustrate the performance of the adaptive space-time splitting scheme for two representative polycrystallization processes. (C) 2021 Elsevier B.V. All rights reserved.
NSTL
Elsevier
