Numerical Linear Algebra for the Two-Dimensional Bertozzi-Esedoglu-Gillette-Cahn-Hilliard Equation in Image Inpainting

被引：0

作者：

Awad, Yahia ^{[1
]}

Fakih, Hussein ^{[1
,2
,3
]}

Alkhezi, Yousuf ^{[4
]}

机构：

[1] Lebanese Int Univ LIU, Dept Math & Phys, Bekaa Campus,POB 5, Al Khyara, Lebanon

[2] Int Univ Beirut BIU, Dept Math & Phys, Beirut Campus,POB 1001, Beirut, Lebanon

[3] Lebanese Univ, Dept Math, Khawarizmi Lab Math & Applicat, POB 1001, Beirut, Lebanon

[4] Publ Author Appl Educ & Training PAAET, Coll Basic Educ, Math Dept, POB 34053, Kuwait 70654, Kuwait

来源：

MATHEMATICS | 2023年 / 11卷 / 24期

关键词：

Cahn-Hilliard equation; image inpainting; finite difference method; numerical linear algebra; stability; steady state;

D O I：

10.3390/math11244952

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we present a numerical linear algebra analytical study of some schemes for the Bertozzi-Esedoglu-Gillette-Cahn-Hilliard equation. Both 1D and 2D finite difference discretizations in space are proposed with semi-implicit and implicit discretizations on time. We prove that our proposed numerical solutions converge to continuous solutions.

引用

页数：31

共 16 条

[1] On the Bertozzi-Esedoglu-Gillette-Cahn-Hilliard Equation with Logarithmic Nonlinear Terms
Cherfils, Laurence
Fakih, Hussein
Miranville, Alain
SIAM JOURNAL ON IMAGING SCIENCES, 2015, 8 (02): : 1123 - 1140
[2] FINITE-DIMENSIONAL ATTRACTORS FOR THE BERTOZZI--ESEDOGLU--GILLETTE--CAHN--HILLIARD EQUATION IN IMAGE INPAINTING
Cherfils, Laurence
Fakih, Hussein
Miranville, Alain
INVERSE PROBLEMS AND IMAGING, 2015, 9 (01) : 105 - 125
[3] CONSERVATIVE STOCHASTIC TWO-DIMENSIONAL CAHN-HILLIARD EQUATION
Rockner, Michael
Yang, Huanyu
Zhu, Rongchan
ANNALS OF APPLIED PROBABILITY, 2021, 31 (03): : 1336 - 1375
[4] Nonlinear Multigrid Implementation for the Two-Dimensional Cahn-Hilliard Equation
Lee, Chaeyoung
Jeong, Darae
Yang, Junxiang
Kim, Junseok
MATHEMATICS, 2020, 8 (01)
[5] A NONCONFORMING FINITE-ELEMENT METHOD FOR THE TWO-DIMENSIONAL CAHN-HILLIARD EQUATION
ELLIOTT, CM
FRENCH, DA
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1989, 26 (04) : 884 - 903
[6] The persistence of phase-separation in LiFePO4 with two-dimensional Li+ transport: The Cahn-Hilliard-reaction equation and the role of defects
Dargaville, S.
Farrell, T. W.
ELECTROCHIMICA ACTA, 2013, 94 : 143 - 158
[7] NUMERICAL SIMULATIONS FOR THE VARIABLE ORDER TWO-DIMENSIONAL REACTION SUB-DIFFUSION EQUATION: LINEAR AND NONLINEAR
Adel, Mohamed
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2022, 30 (01)
[8] Numerical errors of explicit finite difference approximation for two-dimensional solute transport equation with linear sorption
Ataie-Ashtiani, B
Hosseini, SA
ENVIRONMENTAL MODELLING & SOFTWARE, 2005, 20 (07) : 817 - 826
[9] Local Discontinuous Galerkin Methods with Generalized Alternating Numerical Fluxes for Two-dimensional Linear Sobolev Equation
Zhao, Di
Zhang, Qiang
JOURNAL OF SCIENTIFIC COMPUTING, 2019, 78 (03) : 1660 - 1690
[10] Local Discontinuous Galerkin Methods with Generalized Alternating Numerical Fluxes for Two-dimensional Linear Sobolev Equation
Di Zhao
Qiang Zhang
Journal of Scientific Computing, 2019, 78 : 1660 - 1690

← 1 2 →