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A nonstiff, adaptive mesh refinement-based method for the Cahn-Hilliard equation
 

Summary: A nonstiff, adaptive mesh refinement-based
method for the Cahn-Hilliard equation
Hector D. Ceniceros
Department of Mathematics, University of California Santa Barbara , CA 93106
Alexandre M. Roma
Departamento de Matem´atica Aplicada, Universidade de S~ao Paulo, Caixa Postal
66281, CEP 05311-970, S~ao Paulo-SP, Brasil.
Abstract
We present a nonstiff, fully adaptive mesh refinement-based method for the Cahn-
Hilliard equation. The method is based on a semi-implicit splitting, in which linear
leading order terms are extracted and discretized implicitly, combined with a ro-
bust adaptive spatial discretization. The fully discretized equation is written as
a system which is efficiently solved on composite adaptive grids using the linear
multigrid method without any constraint on the time step size. We demonstrate
the efficacy of the method with numerical examples. Both the transient stage and
the steady state solutions of spinodal decompositions are captured accurately with
the proposed adaptive strategy. Employing this approach, we also identify several
stationary solutions of that decomposition on the 2D torus.
Key words: adaptive method, conservative phase field models, spinodal
decomposition, adaptive mesh refinements, semi-implicit methods, multilevel

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics