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Title: First and second order operator splitting methods for the phase field crystal equation

In this paper, we present operator splitting methods for solving the phase field crystal equation which is a model for the microstructural evolution of two-phase systems on atomic length and diffusive time scales. A core idea of the methods is to decompose the original equation into linear and nonlinear subequations, in which the linear subequation has a closed-form solution in the Fourier space. We apply a nonlinear Newton-type iterative method to solve the nonlinear subequation at the implicit time level and thus a considerably large time step can be used. By combining these subequations, we achieve the first- and second-order accuracy in time. We present numerical experiments to show the accuracy and efficiency of the proposed methods.
Authors:
;  [1] ;  [2]
  1. Institute of Mathematical Sciences, Ewha Womans University, Seoul 120-750 (Korea, Republic of)
  2. Department of Mathematics, Ewha Womans University, Seoul 120-750 (Korea, Republic of)
Publication Date:
OSTI Identifier:
22465667
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 299; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; CRYSTALS; EQUATIONS; ITERATIVE METHODS; MATHEMATICAL SOLUTIONS; MICROSTRUCTURE; NONLINEAR PROBLEMS