Department of Mathematics

Applied Mathematics

  •  Linearly Preconditioned Nonlinear Solvers for Phase Field Equations
  •  02/06/2017
  •  10:00 AM - 11:00 AM
  •  C100 Wells Hall
  •  Wenqiang Feng, The University of Tennessee, Knoxville

Many unconditionally energy stable schemes for the physical models will lead to a highly nonlinear elliptic PDE systems which arise from time discretization of parabolic equations. I will discuss two efficient and practical preconditioned solvers- Preconditioned Steepest Descent (PSD) solver and Preconditioned Nonlinear Conjugate Gradient (PNCG) solver - for the nonlinear elliptic PDE systems. The main idea of the preconditioned solvers is to use a linearized version of the nonlinear operator as a pre-conditioner, or in other words, as a metric for choosing the search direction. Based on certain reasonable assumptions of the linear pre-conditioner, a geometric convergence rate is shown for the nonlinear PSD iteration. Numerical simulations for some important physical application problems - including Cahn-Hillilard equation, epitaxial thin film equation with slope selection, square phase field crystal equation and Functionalized Cahn-Hilliard equation- are carried out to verify the efficiency of the solvers.



Department of Mathematics
Michigan State University
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