Computer Science ›› 2023, Vol. 50 ›› Issue (11): 23-31.doi: 10.11896/jsjkx.220800030
• High Performance Computing • Previous Articles Next Articles
GUO Jing1, QI Deyu2
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[1]CAHN J W,HILLIARD J E.Free Energy of a Nonuniform System.I.Interfacial Free Energy[J].The Journal of Chemical Physics,1958,28(2):258-267. [2]CAHN J W.Free Energy of a Nonuniform System.II.Thermodynamic Basis[J].The Journal of Chemical Physics,1959,30(5):1121-1124. [3]ZHOU B,POWELL A C.Phase Field Simulations of Early Stage Structure Formation During Immersion Precipitation of Polymeric Membranes in 2D and 3D[J].Journal of Membrane Science,2006,268(2):150-164. [4]GARCKE H,LAM K F,SITKA E,et al.A Cahn-Hilliard-Darcy Model for Tumour Growth with Chemotaxis and Active Transport[J].Mathematical Models and Methods in Applied Sciences,2016,26(6):1095-1148. [5]QIAN T,WANG X P,SHENG P.A Variational Approach to Moving Contact Line Hydrodynamics[J].Journal of Fluid Mechanics,2006,564:333-360. [6]BERTOZZI A L,ESEDOGLU S,GILLETTE A.Inpainting of Binary Images Using the Cahn-Hilliard Equation[J].IEEE Transactions on Image Processing,2006,16(1):285-291. [7]LAM K F,WU H.Thermodynamically ConsistentNavier-Stokes-Cahn-Hilliard Models with Mass Transfer and Chemotaxis[J].European Journal of Applied Mathematics,2018,29(4):595-644. [8]GUO J,WANG C,WISE S M,et al.An H2 Convergence of a Second-Order Convex-Splitting,Finite Difference Scheme for the Three-Dimensional Cahn-Hilliard Equation[J].Communications in Mathematical Sciences,2016,14:489-515. [9]HU Z,WISE S,WANG C,et al.Stable and Efficient Finite-Difference Nonlinear-Multigrid Schemes for the Phase-Field Crystal Equation[J].Journal of Computational Physics,2009,228:5323-5339. [10]WISE S M.Unconditionally Stable Finite Difference,Nonlinear Multigrid Simulation of the Cahn-Hilliard-Hele-Shaw System of Equations[J].Journal of Scientific Computing,2010,44:38-68. [11]LEE C,JEONG D,YANG J,et al.Nonlinear Multigrid Implementation for the Two-Dimensional Cahn Equation[J].Mathematics,2020,8(1):97. [12]REUSKEN A.Convergence of the Multilevel FullApproxima-tion Scheme Including the V-cycle[J].Numerische Mathematik,1988,53(6):663-686. [13]HACKBUSCH W,REUSKEN A.On Global Multigrid Convergence for Nonlinear Problems[J].Vieweg+Teubner Verlag,1989,23:105-113. [14]HACKBUSCH W,REUSKEN A.Analysis of a Damped Nonlinear Multilevel Method[J].Numerische Mathematik,1989,55(2):225-246. [15]XIE D.New Parallel Iteration Methods,New Nonlinear Multigrid Analysis,and Application in Computational Chemistry[D].Houston:University of Houston,1995. [16]SHAJDUROV V V.Multigrid Methods for Finite Elements[M].Netherlands:Springer,1996:542-543. [17]REUSKEN A.Convergence of the Multigrid Full Approximation Scheme for a Class of Elliptic Mildly Nonlinear Boundary Value Problems[J].Numerische Mathematik,1987,52(3):251-277. [18]HACKBUSCH W.Multi-grid Methods and Applications[M].Berlin:Springer-Verlag 1985. [19]XIE H H,XIE M T,ZHANG N.An Efficient Multigrid Method for Semilinear Elliptic Equation[J].Journal on Numerical methods and computer applications,2019,40(2):143-160. [20]TAI X C,XU J C.Global and Uniform Convergence of Subspace Correction Methods for some Convex Optimization Problems[J].Mathematics of Computation,2002(71):105-124. [21]TAI X C,XU J.Subspace Correction Methods for Convex Opti-mization Problems[C]//Eleventh International Conference on Domain Decomposition Methods.1998. [22]XU J.Iterative Methods by Space Decomposition and SubspaceCorrection[J].Siam Review,1992,34:581-613. [23]CHEN L,HU X,WISE S M.Convergence Analysis of the Fast Subspace Descent Method for Convex Optimization Problems[J].Mathematics of Computation,2020,89(325):2249-2282. [24]EYRE D.Unconditionally Gradient Stable Time Marching theCahn-Hilliard Equation[C]//Computational and Mathematical Models of Microstructural Evolution.Materials Research Society.1998:1686-1712. [25]WISE S M,WANG C,LOWENGRUB J S.An Energy Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation[J].SIAM Journal of Numerical Analysis,2009,47:2269-2288. [26]TROTTENBERG U,OOSTERLEE C W,SCHÜLLER A.Multigrid[M].New York:Academic Press,2005. |
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