A numerical algorithm for the solution of a phase-field model of polycrystalline materials

Authors:
M. R. Dorr;J. -L. Fattebert;M. E. Wickett;J. F. Belak;P. E. A. Turchi
Affiliations:
Center for Applied Scientific Computing, L-561, United States and Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550, United States;Center for Applied Scientific Computing, L-561, United States and Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550, United States;Center for Applied Scientific Computing, L-561, United States and Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550, United States;Condensed Matter and Materials Division, L-045, United States and Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550, United States;Condensed Matter and Materials Division, L-352, United States and Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550, United States
Venue:
Journal of Computational Physics
Year:
2010

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Abstract

We describe an algorithm for the numerical solution of a phase-field model (PFM) of microstructure evolution in polycrystalline materials. The PFM system of equations includes a local order parameter, a quaternion representation of local orientation and a species composition parameter. The algorithm is based on the implicit integration of a semidiscretization of the PFM system using a backward difference formula (BDF) temporal discretization combined with a Newton-Krylov algorithm to solve the nonlinear system at each time step. The BDF algorithm is combined with a coordinate-projection method to maintain quaternion unit length, which is related to an important solution invariant. A key element of the Newton-Krylov algorithm is the selection of a preconditioner to accelerate the convergence of the Generalized Minimum Residual algorithm used to solve the Jacobian linear system in each Newton step. Results are presented for the application of the algorithm to 2D and 3D examples.