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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
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- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.21 No.1
- 발행연도
- 2017.3
- 수록면
- 1 - 16 (16page)
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초록· 키워드
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The Allen–Cahn equation is solved numerically by operator splitting Fourier spectral methods. The basic idea of the operator splitting method is to decompose the original problem into sub-equations and compose the approximate solution of the original equation using the solutions of the subproblems. The purpose of this paper is to characterize higher order operator splitting schemes and propose several higher order methods. Unlike the first and the second order methods, each of the heat and the free-energy evolution operators has at least one backward evaluation in higher order methods. We investigate the effect of negative time steps on a general form of third order schemes and suggest three third order methods for better stability and accuracy. Two fourth order methods are also presented. The traveling wave solution and a spinodal decomposition problem are used to demonstrate numerical properties and the order of convergence of the proposed methods.
목차
ABSTRACT
1. INTRODUCTION
2. A BRIEF REVIEW ON THE OPERATOR SPLITTING METHOD
3. HIGHER-ORDER OPERATOR SPLITTING FOURIER SPECTRAL METHODS
4. NUMERICAL EXPERIMENTS
5. CONCLUSIONS
REFERENCES
참고문헌 (26)
참고문헌 신청
[학술지(정기간행물)] - S.M. Allen / 1979 / A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening / Acta Metallurgica 27 : 1085 ~ 1095
[학술지(정기간행물)] - M. Benes / 2004 / Geometrical image segmentation by the Allen–Cahn equation / Applied Numerical Mathematics 51 : 187 ~ 205
[학술지(정기간행물)] - J.A. Dobrosotskaya / 2008 / A wavelet-Laplace variational technique for image deconvolution and inpainting / IEEE Transactions on Image Processing 17 : 657 ~ 663
[학술지(정기간행물)] - L.C. Evans / 1992 / Phase transitions and generalized motion by mean curvature / Communications on Pure and Applied Mathematics 45 : 1097 ~ 1123
[학술지(정기간행물)] - X. Feng / 2003 / Numerical analysis of the Allen–Cahn equation and approximation for mean curvature flows / Numerische Mathematik 94 : 33 ~ 65
[학술지(정기간행물)] - M. Benes / 2004 / Geometrical image segmentation by the Allen–Cahn equation / Applied Numerical Mathematics 51 : 187 ~ 205
[학술지(정기간행물)] - J.A. Dobrosotskaya / 2008 / A wavelet-Laplace variational technique for image deconvolution and inpainting / IEEE Transactions on Image Processing 17 : 657 ~ 663
[학술지(정기간행물)] - L.C. Evans / 1992 / Phase transitions and generalized motion by mean curvature / Communications on Pure and Applied Mathematics 45 : 1097 ~ 1123
[학술지(정기간행물)] - X. Feng / 2003 / Numerical analysis of the Allen–Cahn equation and approximation for mean curvature flows / Numerische Mathematik 94 : 33 ~ 65
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UCI(KEPA) : I410-ECN-0101-2017-410-002303581