An Adaptive Time-Stepping Strategy for the Molecular Beam Epitaxy Models

This paper is concerned with the numerical simulations for the dynamics of the molecular beam epitaxy (MBE) model. The numerical simulations of the MBE models require long time computations, and therefore large time-stepping methods become necessary. In this work, we consider some unconditionally en...

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Bibliographic Details
Published in:SIAM journal on scientific computing Vol. 33; no. 3; pp. 1395 - 1414
Main Authors: Qiao, Zhonghua, Zhang, Zhengru, Tang, Tao
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2011
Subjects:
Computation
Computer simulation
Dynamics
Energy use
Exact sciences and technology
Mathematical analysis
Mathematical models
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Molecular beam epitaxy
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Sciences and techniques of general use
Simulation
Strategy
Studies
molecular beam epitaxy
adaptive time-stepping method
finite difference schemes
35Q99
Numerical method
Stochastic method
Adaptive method
Computation time
Numerical analysis
unconditionally energy stable
Scientific computation
65M70
35R99
Numerical simulation
Simulation model
Steady state solution
65M12
Finite difference method
ISSN:1064-8275, 1095-7197
Online Access:Get full text
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Summary:This paper is concerned with the numerical simulations for the dynamics of the molecular beam epitaxy (MBE) model. The numerical simulations of the MBE models require long time computations, and therefore large time-stepping methods become necessary. In this work, we consider some unconditionally energy stable finite difference schemes, which will be used in the time adaptivity strategies. It is found that the use of the time adaptivity cannot only resolve the steady-state solutions but also the dynamical changes of the solution accurately and efficiently. The adaptive time step is selected based on the energy variation or the change of the roughness of the solution. The numerical experiments demonstrated that the CPU time is significantly saved for long time simulations. [PUBLICATION ABSTRACT]
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ISSN:1064-8275
1095-7197
DOI:10.1137/100812781