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Title: An adaptive time-stepping strategy for solving the phase field crystal model

In this work, we will propose an adaptive time step method for simulating the dynamics of the phase field crystal (PFC) model. The numerical simulation of the PFC model needs long time to reach steady state, and then large time-stepping method is necessary. Unconditionally energy stable schemes are used to solve the PFC model. The time steps are adaptively determined based on the time derivative of the corresponding energy. It is found that the use of the proposed time step adaptivity cannot only resolve the steady state solution, but also the dynamical development of the solution efficiently and accurately. The numerical experiments demonstrate that the CPU time is significantly saved for long time simulations.
Authors:
 [1] ;  [2] ;  [3]
  1. Laboratory of Mathematics and Complex Systems, Ministry of Education and School of Mathematical Sciences, Beijing Normal University, Beijing 100875 (China)
  2. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong (Hong Kong)
  3. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon (Hong Kong)
Publication Date:
OSTI Identifier:
22230792
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 249; Other Information: Copyright (c) 2013 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:
97 MATHEMATICAL METHODS AND COMPUTING; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; COMPUTERIZED SIMULATION; CRYSTAL MODELS; CRYSTALS; MATHEMATICAL SOLUTIONS; STEADY-STATE CONDITIONS