A numerical algorithm for the solution of a phase-field model of polycrystalline materials
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...
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| Veröffentlicht in: | Journal of computational physics 2010-02, Vol.229 (3), p.626-641 |
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| container_title | Journal of computational physics |
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| creator | Dorr, M.R. Fattebert, J.-L. Wickett, M.E. Belak, J.F. Turchi, P.E.A. |
| description | 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. |
| doi_str_mv | 10.1016/j.jcp.2009.09.041 |
| format | Article |
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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. 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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. 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| source | Elsevier ScienceDirect Journals |
| subjects | Computational techniques Exact sciences and technology Mathematical methods in physics Method of lines Newton–Krylov methods Phase-field model Physics Polycrystalline microstructure |
| title | A numerical algorithm for the solution of a phase-field model of polycrystalline materials |
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