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An unconditionally stable spectral m...

Halliwell, Garry T.

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An unconditionally stable spectral method for an isotropic thin-film equation.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	An unconditionally stable spectral method for an isotropic thin-film equation./
Author:	Halliwell, Garry T.
Description:	79 p.
Notes:	Source: Dissertation Abstracts International, Volume: 74-06(E), Section: B.
Contained By:	Dissertation Abstracts International74-06B(E).
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3554452
ISBN:	9781267946034

An unconditionally stable spectral method for an isotropic thin-film equation.
Halliwell, Garry T.

An unconditionally stable spectral method for an isotropic thin-film equation. - 79 p.

Source: Dissertation Abstracts International, Volume: 74-06(E), Section: B.

Thesis (Ph.D.)--State University of New York at Buffalo, 2013.

Mathematical models for thin-film evolution equations and their coarsening behavior have been extensively studied, however a challenge for computer simulations is finding time stepping algorithms that evolve large systems to long times. The thin solid film model is a nonlinear, fourth order, parabolic partial differential equation that is first order in time. Using a semi-implicit operator splitting spectral method, we developed an algorithm that is unconditionally stable allowing arbitrarily large time steps. Stability was achieved by von Neumann analysis resulting in an adaptive parametrization of the splitting at each time step. The novel aspect of this work relative to similar work done on other coarsening models, e.g. the Cahn-Hilliard equation, is the treatment of non-local and inverse power terms. Our numerical method is robust and accurate, with coarsening results orders of magnitude shorter in computation time than Euler's Method.

ISBN: 9781267946034Subjects--Topical Terms:

515831
Mathematics.

An unconditionally stable spectral method for an isotropic thin-film equation.
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100 1 $a Halliwell, Garry T. $3 2094914
245 1 3 $a An unconditionally stable spectral method for an isotropic thin-film equation.
300 $a 79 p.
500 $a Source: Dissertation Abstracts International, Volume: 74-06(E), Section: B.
500 $a Adviser: Brian J. Spencer.
502 $a Thesis (Ph.D.)--State University of New York at Buffalo, 2013.
520 $a Mathematical models for thin-film evolution equations and their coarsening behavior have been extensively studied, however a challenge for computer simulations is finding time stepping algorithms that evolve large systems to long times. The thin solid film model is a nonlinear, fourth order, parabolic partial differential equation that is first order in time. Using a semi-implicit operator splitting spectral method, we developed an algorithm that is unconditionally stable allowing arbitrarily large time steps. Stability was achieved by von Neumann analysis resulting in an adaptive parametrization of the splitting at each time step. The novel aspect of this work relative to similar work done on other coarsening models, e.g. the Cahn-Hilliard equation, is the treatment of non-local and inverse power terms. Our numerical method is robust and accurate, with coarsening results orders of magnitude shorter in computation time than Euler's Method.
590 $a School code: 0656.
650 4 $a Mathematics. $3 515831
650 4 $a Nanoscience. $3 587832
650 4 $a Applied Mathematics. $3 1669109
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710 2 $a State University of New York at Buffalo. $b Mathematics. $3 1022476
773 0 $t Dissertation Abstracts International $g 74-06B(E).
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793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3554452