Cheng, Kelong; Wang, Cheng; Wise, Steven M. High order accurate and convergent numerical scheme for the strongly anisotropic Cahn-Hilliard model. (English) Zbl 07777387 Numer. Methods Partial Differ. Equations 39, No. 5, 4007-4029 (2023). MSC: 65M70 65M06 65N35 35B65 41A21 31A30 35Q74 PDFBibTeX XMLCite \textit{K. Cheng} et al., Numer. Methods Partial Differ. Equations 39, No. 5, 4007--4029 (2023; Zbl 07777387) Full Text: DOI
Liu, Chun; Wang, Cheng; Wise, Steven M.; Yue, Xingye; Zhou, Shenggao A second order accurate, positivity preserving numerical method for the Poisson-Nernst-Planck system and its convergence analysis. (English) Zbl 07751604 J. Sci. Comput. 97, No. 1, Paper No. 23, 35 p. (2023). MSC: 65-XX 35K35 35K55 65M06 65M12 PDFBibTeX XMLCite \textit{C. Liu} et al., J. Sci. Comput. 97, No. 1, Paper No. 23, 35 p. (2023; Zbl 07751604) Full Text: DOI arXiv
Park, Jea-Hyun; Salgado, Abner J.; Wise, Steven M. Benchmark computations of the phase field crystal and functionalized Cahn-Hilliard equations via fully implicit, Nesterov accelerated schemes. (English) Zbl 1512.74099 Commun. Comput. Phys. 33, No. 2, 367-398 (2023). MSC: 74S25 74S20 74N99 74E15 PDFBibTeX XMLCite \textit{J.-H. Park} et al., Commun. Comput. Phys. 33, No. 2, 367--398 (2023; Zbl 1512.74099) Full Text: DOI arXiv
Chen, Xiaochun; Wang, Cheng; Wise, Steven M. A preconditioned steepest descent solver for the Cahn-Hilliard equation with variable mobility. (English) Zbl 1513.65278 Int. J. Numer. Anal. Model. 19, No. 6, 839-863 (2022). MSC: 65M06 65M12 35K30 PDFBibTeX XMLCite \textit{X. Chen} et al., Int. J. Numer. Anal. Model. 19, No. 6, 839--863 (2022; Zbl 1513.65278) Full Text: Link
Yuan, Maoqin; Chen, Wenbin; Wang, Cheng; Wise, Steven M.; Zhang, Zhengru A second order accurate in time, energy stable finite element scheme for the Flory-Huggins-Cahn-Hilliard equation. (English) Zbl 1513.35293 Adv. Appl. Math. Mech. 14, No. 6, 1477-1508 (2022). MSC: 35K25 35K55 60F10 65M60 PDFBibTeX XMLCite \textit{M. Yuan} et al., Adv. Appl. Math. Mech. 14, No. 6, 1477--1508 (2022; Zbl 1513.35293) Full Text: DOI
Dong, Lixiu; Wang, Cheng; Wise, Steven M.; Zhang, Zhengru Optimal rate convergence analysis of a numerical scheme for the ternary Cahn-Hilliard system with a Flory-Huggins-deGennes energy potential. (English) Zbl 1503.65168 J. Comput. Appl. Math. 415, Article ID 114474, 18 p. (2022). MSC: 65M06 35K35 65M12 65M15 PDFBibTeX XMLCite \textit{L. Dong} et al., J. Comput. Appl. Math. 415, Article ID 114474, 18 p. (2022; Zbl 1503.65168) Full Text: DOI
Cheng, Kelong; Wang, Cheng; Wise, Steven M.; Wu, Yanmei A third order accurate in time, BDF-type energy stable scheme for the Cahn-Hilliard equation. (English) Zbl 1499.65556 Numer. Math., Theory Methods Appl. 15, No. 2, 279-303 (2022). MSC: 65M70 65M12 65M15 PDFBibTeX XMLCite \textit{K. Cheng} et al., Numer. Math., Theory Methods Appl. 15, No. 2, 279--303 (2022; Zbl 1499.65556) Full Text: DOI
Liu, Chun; Wang, Cheng; Wang, Yiwei; Wise, Steven M. Convergence analysis of the variational operator splitting scheme for a reaction-diffusion system with detailed balance. (English) Zbl 07516278 SIAM J. Numer. Anal. 60, No. 2, 781-803 (2022). MSC: 65-XX 35K35 35K55 49J40 65M06 65M12 PDFBibTeX XMLCite \textit{C. Liu} et al., SIAM J. Numer. Anal. 60, No. 2, 781--803 (2022; Zbl 07516278) Full Text: DOI arXiv
Chen, Wenbin; Jing, Jianyu; Wang, Cheng; Wang, Xiaoming; Wise, Steven M. A modified Crank-Nicolson numerical scheme for the Flory-Huggins Cahn-Hilliard model. (English) Zbl 07493157 Commun. Comput. Phys. 31, No. 1, 60-93 (2022). MSC: 65-XX 35K35 35K55 49J40 65K10 65M06 65M12 PDFBibTeX XMLCite \textit{W. Chen} et al., Commun. Comput. Phys. 31, No. 1, 60--93 (2022; Zbl 07493157) Full Text: DOI
Dong, Lixiu; Wang, Cheng; Wise, Steven M.; Zhang, Zhengru A positivity-preserving, energy stable scheme for a ternary Cahn-Hilliard system with the singular interfacial parameters. (English) Zbl 07513797 J. Comput. Phys. 442, Article ID 110451, 29 p. (2021). MSC: 65Mxx 35Kxx 35Qxx PDFBibTeX XMLCite \textit{L. Dong} et al., J. Comput. Phys. 442, Article ID 110451, 29 p. (2021; Zbl 07513797) Full Text: DOI arXiv
Liu, Chun; Wang, Cheng; Wise, Steven M.; Yue, Xingye; Zhou, Shenggao A positivity-preserving, energy stable and convergent numerical scheme for the Poisson-Nernst-Planck system. (English) Zbl 1480.65213 Math. Comput. 90, No. 331, 2071-2106 (2021). MSC: 65M06 65M12 35C20 35K35 35K55 35A01 35B09 49J40 78A57 35Q60 PDFBibTeX XMLCite \textit{C. Liu} et al., Math. Comput. 90, No. 331, 2071--2106 (2021; Zbl 1480.65213) Full Text: DOI arXiv
Yuan, Maoqin; Chen, Wenbin; Wang, Cheng; Wise, Steven M.; Zhang, Zhengru An energy stable finite element scheme for the three-component Cahn-Hilliard-type model for macromolecular microsphere composite hydrogels. (English) Zbl 1473.65219 J. Sci. Comput. 87, No. 3, Paper No. 78, 30 p. (2021). MSC: 65M60 65N30 35K25 35K55 60F10 35Q35 PDFBibTeX XMLCite \textit{M. Yuan} et al., J. Sci. Comput. 87, No. 3, Paper No. 78, 30 p. (2021; Zbl 1473.65219) Full Text: DOI arXiv
Zhang, Juan; Wang, Cheng; Wise, Steven M.; Zhang, Zhengru Structure-preserving, energy stable numerical schemes for a liquid thin film coarsening model. (English) Zbl 1468.65119 SIAM J. Sci. Comput. 43, No. 2, A1248-A1272 (2021). MSC: 65M06 65M12 76A20 35K35 35K55 49J40 PDFBibTeX XMLCite \textit{J. Zhang} et al., SIAM J. Sci. Comput. 43, No. 2, A1248--A1272 (2021; Zbl 1468.65119) Full Text: DOI arXiv
Guo, Jing; Wang, Cheng; Wise, Steven M.; Yue, Xingye An improved error analysis for a second-order numerical scheme for the Cahn-Hilliard equation. (English) Zbl 1459.65141 J. Comput. Appl. Math. 388, Article ID 113300, 17 p. (2021). MSC: 65M06 35K30 65M12 65M15 65T40 PDFBibTeX XMLCite \textit{J. Guo} et al., J. Comput. Appl. Math. 388, Article ID 113300, 17 p. (2021; Zbl 1459.65141) Full Text: DOI
Zhang, Chenhui; Ouyang, Jie; Wang, Cheng; Wise, Steven M. Numerical comparison of modified-energy stable SAV-type schemes and classical BDF methods on benchmark problems for the functionalized Cahn-Hilliard equation. (English) Zbl 07508401 J. Comput. Phys. 423, Article ID 109772, 35 p. (2020). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{C. Zhang} et al., J. Comput. Phys. 423, Article ID 109772, 35 p. (2020; Zbl 07508401) Full Text: DOI
Cheng, Kelong; Wang, Cheng; Wise, Steven M. A weakly nonlinear, energy stable scheme for the strongly anisotropic Cahn-Hilliard equation and its convergence analysis. (English) Zbl 1453.65268 J. Comput. Phys. 405, Article ID 109109, 28 p. (2020). MSC: 65M12 65M22 35B10 PDFBibTeX XMLCite \textit{K. Cheng} et al., J. Comput. Phys. 405, Article ID 109109, 28 p. (2020; Zbl 1453.65268) Full Text: DOI
Chen, Wenbin; Wang, Cheng; Wang, Shufen; Wang, Xiaoming; Wise, Steven M. Energy stable numerical schemes for ternary Cahn-Hilliard system. (English) Zbl 1447.65098 J. Sci. Comput. 84, No. 2, Paper No. 27, 36 p. (2020). MSC: 65M70 65M06 65L06 65M12 35K30 35K55 65K10 35R09 PDFBibTeX XMLCite \textit{W. Chen} et al., J. Sci. Comput. 84, No. 2, Paper No. 27, 36 p. (2020; Zbl 1447.65098) Full Text: DOI
Chen, Wenbin; Wang, Cheng; Wang, Xiaoming; Wise, Steven M. Positivity-preserving, energy stable numerical schemes for the Cahn-Hilliard equation with logarithmic potential. (English) Zbl 07785514 J. Comput. Phys.: X 3, Article ID 100031, 29 p. (2019). MSC: 65Mxx 35Kxx 35Qxx PDFBibTeX XMLCite \textit{W. Chen} et al., J. Comput. Phys.: X 3, Article ID 100031, 29 p. (2019; Zbl 07785514) Full Text: DOI arXiv
Cheng, Kelong; Wang, Cheng; Wise, Steven M. An energy stable BDF2 Fourier pseudo-spectral numerical scheme for the square phase field crystal equation. (English) Zbl 1518.65115 Commun. Comput. Phys. 26, No. 5, 1335-1364 (2019). MSC: 65M70 65M06 65N35 65K10 65F08 65B05 65M12 41A25 35K30 35K55 74N05 82D25 35Q74 35Q82 PDFBibTeX XMLCite \textit{K. Cheng} et al., Commun. Comput. Phys. 26, No. 5, 1335--1364 (2019; Zbl 1518.65115) Full Text: DOI arXiv
Church, Jon Matteo; Guo, Zhenlin; Jimack, Peter K.; Madzvamuse, Anotida; Promislow, Keith; Wetton, Brian; Wise, Steven M.; Yang, Fengwei High accuracy benchmark problems for Allen-Cahn and Cahn-Hilliard dynamics. (English) Zbl 1473.65099 Commun. Comput. Phys. 26, No. 4, 947-972 (2019). MSC: 65M06 65M70 PDFBibTeX XMLCite \textit{J. M. Church} et al., Commun. Comput. Phys. 26, No. 4, 947--972 (2019; Zbl 1473.65099) Full Text: DOI
Cheng, Kelong; Feng, Wenqiang; Wang, Cheng; Wise, Steven M. An energy stable fourth order finite difference scheme for the Cahn-Hilliard equation. (English) Zbl 1416.65256 J. Comput. Appl. Math. 362, 574-595 (2019). MSC: 65M06 35K35 35K55 65K10 65M12 PDFBibTeX XMLCite \textit{K. Cheng} et al., J. Comput. Appl. Math. 362, 574--595 (2019; Zbl 1416.65256) Full Text: DOI arXiv
Chen, Wenbin; Feng, Wenqiang; Liu, Yuan; Wang, Cheng; Wise, Steven M. A second order energy stable scheme for the Cahn-Hilliard-Hele-Shaw equations. (English) Zbl 1407.65097 Discrete Contin. Dyn. Syst., Ser. B 24, No. 1, 149-182 (2019). MSC: 65M06 65M12 35K55 76D05 35Q35 76D27 76S05 65N55 65L06 PDFBibTeX XMLCite \textit{W. Chen} et al., Discrete Contin. Dyn. Syst., Ser. B 24, No. 1, 149--182 (2019; Zbl 1407.65097) Full Text: DOI arXiv
Yan, Yue; Chen, Wenbin; Wang, Cheng; Wise, Steven M. A second-order energy stable BDF numerical scheme for the Cahn-Hilliard equation. (English) Zbl 1488.65367 Commun. Comput. Phys. 23, No. 2, 572-602 (2018). MSC: 65M12 65M60 35K35 35K55 PDFBibTeX XMLCite \textit{Y. Yan} et al., Commun. Comput. Phys. 23, No. 2, 572--602 (2018; Zbl 1488.65367) Full Text: DOI
Dong, Lixiu; Feng, Wenqiang; Wang, Cheng; Wise, Steven M.; Zhang, Zhengru Convergence analysis and numerical implementation of a second order numerical scheme for the three-dimensional phase field crystal equation. (English) Zbl 1409.82014 Comput. Math. Appl. 75, No. 6, 1912-1928 (2018). MSC: 82C80 65M06 65M12 82D25 82C26 PDFBibTeX XMLCite \textit{L. Dong} et al., Comput. Math. Appl. 75, No. 6, 1912--1928 (2018; Zbl 1409.82014) Full Text: DOI arXiv
Cheng, Kelong; Wang, Cheng; Wise, Steven M.; Yue, Xingye A second-order, weakly energy-stable pseudo-spectral scheme for the Cahn-Hilliard equation and its solution by the homogeneous linear iteration method. (English) Zbl 1375.65137 J. Sci. Comput. 69, No. 3, 1083-1114 (2016). Reviewer: K. N. Shukla (Gurgaon) MSC: 65M70 35Q35 65M12 65T50 PDFBibTeX XMLCite \textit{K. Cheng} et al., J. Sci. Comput. 69, No. 3, 1083--1114 (2016; Zbl 1375.65137) Full Text: DOI
Guan, Zhen; Heinonen, Vili; Lowengrub, John; Wang, Cheng; Wise, Steven M. An energy stable, hexagonal finite difference scheme for the 2D phase field crystal amplitude equations. (English) Zbl 1349.74360 J. Comput. Phys. 321, 1026-1054 (2016). MSC: 74S20 65M06 74E15 82D25 PDFBibTeX XMLCite \textit{Z. Guan} et al., J. Comput. Phys. 321, 1026--1054 (2016; Zbl 1349.74360) Full Text: DOI
Guan, Zhen; Lowengrub, John S.; Wang, Cheng; Wise, Steven M. Second order convex splitting schemes for periodic nonlocal Cahn-Hilliard and Allen-Cahn equations. (English) Zbl 1349.65298 J. Comput. Phys. 277, 48-71 (2014). MSC: 65M06 35B10 35R09 65R20 45K05 65M12 PDFBibTeX XMLCite \textit{Z. Guan} et al., J. Comput. Phys. 277, 48--71 (2014; Zbl 1349.65298) Full Text: DOI
Chen, Wenbin; Wang, Cheng; Wang, Xiaoming; Wise, Steven M. A linear iteration algorithm for a second-order energy stable scheme for a thin film model without slope selection. (English) Zbl 1305.82034 J. Sci. Comput. 59, No. 3, 574-601 (2014). Reviewer: Mei Yin (Denver) MSC: 82B80 35G20 65M70 82-08 PDFBibTeX XMLCite \textit{W. Chen} et al., J. Sci. Comput. 59, No. 3, 574--601 (2014; Zbl 1305.82034) Full Text: DOI
Baskaran, Arvind; Hu, Zhengzheng; Lowengrub, John S.; Wang, Cheng; Wise, Steven M.; Zhou, Peng Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation. (English) Zbl 1349.65265 J. Comput. Phys. 250, 270-292 (2013). MSC: 65M06 74E15 PDFBibTeX XMLCite \textit{A. Baskaran} et al., J. Comput. Phys. 250, 270--292 (2013; Zbl 1349.65265) Full Text: DOI arXiv