An Adaptive, Multilevel Scheme for the Implicit Solution of Three-Dimensional Phase-Field Equations

作者：Green J R; Jimack P K^*; Mullis A M; Rosam J

来源：Numerical Methods for Partial Differential Equations, 2011, 27(1): 106-120.

DOI：10.1002/num.20634

• adaptive methods
• multigrid methods
• multiscale problems
• nonlinear partial differential equations
• phase change problems
• phase field models
• stiff systems

Phase field models consisting of a set of highly nonlinear coupled parabolic partial differential equations are widely used for the simulation of a range of solidification phenomena This article focuses on the numerical solution of one such model, representing anisotropic solidification in three space dimensions The main contribution of the work is to propose a solution strategy that combines hierarchical mesh adaptivity with implicit time integration and the use of a nonlinear multigrid solver at each step This strategy is implemented in a general software framework that permits parallel computation in a n

• 出版日期2011-1