A Numerical Algorithm for the Solution of a Phase-Field Model of Polycrystalline Materials

Journal Article · Thu Dec 04 04:00:00 EST 2008 · Journal of Computational Physics

OSTI ID:972412

Dorr, M R; Fattebert, J; Wickett, M E; Belak, J F; Turchi, P A

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.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA
• Sponsoring Organization: USDOE
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 972412
• Report Number(s): LLNL-JRNL-409478
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 3 Vol. 229; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
99 GENERAL AND MISCELLANEOUS
ALGORITHMS
CONVERGENCE
MICROSTRUCTURE
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
ORDER PARAMETERS
ORIENTATION