# zbMATH — the first resource for mathematics

## Wise, Steven M.

Compute Distance To:
 Author ID: wise.steven-m Published as: Wise, Steven M.; Wise, S. M.; Wise, Steven
 Documents Indexed: 63 Publications since 1994
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#### Co-Authors

 1 single-authored 35 Wang, Cheng 18 Lowengrub, John Samuel 8 Feng, Wenqiang 7 Chen, Wenbin 6 Cristini, Vittorio 6 Wang, Xiaoming 5 Zhang, Zhengru 4 Cheng, Kelong 4 Guan, Zhen 4 Voigt, Axel 4 Yue, Xingye 3 Diegel, Amanda E. 3 Frieboes, Hermann B. 3 Guo, Zhenlin 3 Liu, Yuan 3 Salvalaglio, Marco 3 Shen, Jie 2 Aristotelous, Andreas C. 2 Baskaran, Arvind 2 Chuang, Yao-Li 2 Guo, Jing 2 Hu, Zhengzheng 2 Jin, Fang 2 Karakashian, Ohannes A. 2 Lin, Ping 2 Salgado, Abner J. 1 Adi-Kusumo, Fajar 1 Aryati, Lina 1 Backofen, Rainer 1 Chen, Long 1 Chen, Nan 1 Conde, Sidafa 1 Dong, Lixiu 1 Feng, Xiaobing 1 Feng, Xiaobing H. 1 Forde, Jonathan E. 1 Hardianti, Mardiah Suci 1 Heinonen, Vili 1 Houk, James C. 1 Hu, Xiaozhe 1 Kim, Junseok 1 Lenhart, Suzanne M. 1 Lewis, Thomas Lee 1 Li, Xiangrong 1 Li, Xiaofan 1 Liu, Chun 1 Macklin, Paul 1 Noor-Asih, Tri Sri 1 Park, Jea-Hyun 1 Qiao, Zhonghua 1 Rebholz, Leo G. 1 Schaal, Daniel J. 1 Selch, Maximilian 1 Sommese, Andrew John 1 Torabi, Solmaz 1 Wang, Shufen 1 Watson, Layne Terry 1 Xiao, Mengying 1 Yu, Fei 1 Yuan, Maoqin 1 Yuan, Zixia 1 Zhang, Juan 1 Zheng, Xiaoming 1 Zhou, Shenggao
all top 5

#### Serials

 9 Journal of Computational Physics 8 Journal of Scientific Computing 6 SIAM Journal on Numerical Analysis 3 Mathematical Methods in the Applied Sciences 3 Mathematics of Computation 3 Numerische Mathematik 3 Discrete and Continuous Dynamical Systems. Series B 3 International Journal of Numerical Analysis and Modeling 2 IMA Journal of Numerical Analysis 2 Bulletin of Mathematical Biology 2 Journal of Computational and Applied Mathematics 2 Journal of Theoretical Biology 1 Computers & Mathematics with Applications 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Fluid Mechanics 1 Journal of Mathematical Biology 1 Nonlinearity 1 ACM Transactions on Mathematical Software 1 Numerical Methods for Partial Differential Equations 1 Mathematical and Computer Modelling 1 SIAM Journal on Scientific Computing 1 Congressus Numerantium 1 Methods and Applications of Analysis 1 Discrete and Continuous Dynamical Systems 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Communications in Mathematical Sciences 1 Communications in Computational Physics 1 Discrete and Continuous Dynamical Systems. Series S
all top 5

#### Fields

 54 Numerical analysis (65-XX) 38 Partial differential equations (35-XX) 11 Fluid mechanics (76-XX) 10 Statistical mechanics, structure of matter (82-XX) 9 Biology and other natural sciences (92-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 3 Mechanics of deformable solids (74-XX) 3 Classical thermodynamics, heat transfer (80-XX) 1 Combinatorics (05-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX) 1 Quantum theory (81-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH Open

55 Publications have been cited 2,100 times in 746 Documents Cited by Year
An energy-stable and convergent finite-difference scheme for the phase field crystal equation. Zbl 1201.35027
Wise, S. M.; Wang, Cheng; Lowengrub, J. S.
2009
Second-order convex splitting schemes for gradient flows with Ehrlich-Schwoebel type energy: Application to thin film epitaxy. Zbl 1247.65088
Shen, Jie; Wang, Cheng; Wang, Xiaoming; Wise, Steven M.
2012
Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation. Zbl 1171.82015
Hu, Z.; Wise, S. M.; Wang, C.; Lowengrub, J. S.
2009
Nonlinear modelling of cancer: bridging the gap between cells and tumours. Zbl 1181.92046
Lowengrub, J. S.; Frieboes, H. B.; Jin, F.; Chuang, Y-L; Li, X.; Macklin, P.; Wise, S. M.; Cristini, V.
2010
Three-dimensional multispecies nonlinear tumor growth. I: Model and numerical method. Zbl 1398.92135
Wise, S. M.; Lowengrub, J. S.; Frieboes, H. B.; Cristini, Vittorio
2008
An energy stable and convergent finite-difference scheme for the modified phase field crystal equation. Zbl 1230.82005
Wang, C.; Wise, S. M.
2011
Unconditionally stable finite difference, nonlinear multigrid simulation of the Cahn-Hilliard-Hele-Shaw system of equations. Zbl 1203.76153
Wise, S. M.
2010
Nonlinear simulations of solid tumor growth using a mixture model: invasion and branching. Zbl 1311.92039
Cristini, Vittorio; Li, Xiangrong; Lowengrub, John S.; Wise, Steven M.
2009
Unconditionally stable schemes for equations of thin film epitaxy. Zbl 1201.65166
Wang, Cheng; Wang, Xiaoming; Wise, Steven M.
2010
Solving the regularized, strongly anisotropic Cahn-Hilliard equation by an adaptive nonlinear multigrid method. Zbl 1310.82044
Wise, Steven; Kim, Junseok; Lowengrub, John
2007
Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method. Zbl 1334.92214
Zheng, X.; Wise, S. M.; Cristini, V.
2005
Convergence analysis of a second order convex splitting scheme for the modified phase field crystal equation. Zbl 1401.82046
Baskaran, A.; Lowengrub, J. S.; Wang, C.; Wise, S. M.
2013
Second order convex splitting schemes for periodic nonlocal Cahn-Hilliard and Allen-Cahn equations. Zbl 1349.65298
Guan, Zhen; Lowengrub, John S.; Wang, Cheng; Wise, Steven M.
2014
A linear energy stable scheme for a thin film model without slope selection. Zbl 1326.76007
Chen, Wenbin; Conde, Sidafa; Wang, Cheng; Wang, Xiaoming; Wise, Steven M.
2012
Analysis of a Darcy–Cahn–Hilliard diffuse interface model for the Hele-Shaw flow and its fully discrete finite element approximation. Zbl 1426.76258
Feng, Xiaobing; Wise, Steven
2012
Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation. Zbl 1349.65265
Baskaran, Arvind; Hu, Zhengzheng; Lowengrub, John S.; Wang, Cheng; Wise, Steven M.; Zhou, Peng
2013
Analysis of a mixed finite element method for a Cahn-Hilliard-Darcy-Stokes system. Zbl 1330.76065
Diegel, Amanda E.; Feng, Xiaobing H.; Wise, Steven M.
2015
A new phase-field model for strongly anisotropic systems. Zbl 1186.80014
Torabi, Solmaz; Lowengrub, John; Voigt, Axel; Wise, Steven
2009
A linear iteration algorithm for a second-order energy stable scheme for a thin film model without slope selection. Zbl 1305.82034
Chen, Wenbin; Wang, Cheng; Wang, Xiaoming; Wise, Steven M.
2014
An efficient, energy stable scheme for the Cahn-Hilliard-Brinkman system. Zbl 1373.76161
Collins, Craig; Shen, Jie; Wise, Steven M.
2013
An $$H^2$$ convergence of a second-order convex-splitting, finite difference scheme for the three-dimensional Cahn-Hilliard equation. Zbl 1338.65221
Guo, Jing; Wang, Cheng; Wise, Steven M.; Yue, Xingye
2016
Stability and convergence of a second-order mixed finite element method for the Cahn-Hilliard equation. Zbl 1433.80005
Diegel, Amanda E.; Wang, Cheng; Wise, Steven M.
2016
An energy stable fourth order finite difference scheme for the Cahn-Hilliard equation. Zbl 1416.65256
Cheng, Kelong; Feng, Wenqiang; Wang, Cheng; Wise, Steven M.
2019
A convergent convex splitting scheme for the periodic nonlocal Cahn-Hilliard equation. Zbl 1304.65209
Guan, Zhen; Wang, Cheng; Wise, Steven M.
2014
An adaptive multigrid algorithm for simulating solid tumor growth using mixture models. Zbl 1211.65123
Wise, S. M.; Lowengrub, J. S.; Cristini, V.
2011
Convergence analysis of a fully discrete finite difference scheme for the Cahn-Hilliard-Hele-Shaw equation. Zbl 1342.65174
Chen, Wenbin; Liu, Yuan; Wang, Cheng; Wise, Steven M.
2016
Convergence analysis and error estimates for a second order accurate finite element method for the Cahn-Hilliard-Navier-Stokes system. Zbl 06804021
Diegel, Amanda E.; Wang, Cheng; Wang, Xiaoming; Wise, Steven M.
2017
A mixed discontinuous Galerkin, convex splitting scheme for a modified Cahn-Hilliard equation and an efficient nonlinear multigrid solver. Zbl 1278.65149
Aristotelous, Andreas C.; Karakashian, Ohannes; Wise, Steven M.
2013
A second-order, weakly energy-stable pseudo-spectral scheme for the Cahn-Hilliard equation and its solution by the homogeneous linear iteration method. Zbl 1375.65137
Cheng, Kelong; Wang, Cheng; Wise, Steven M.; Yue, Xingye
2016
Three-dimensional multispecies nonlinear tumor growth. II: Tumor invasion and angiogenesis. Zbl 1406.92049
Frieboes, Hermann B.; Jin, Fang; Chuang, Yao-Li; Wise, Steven M.; Lowengrub, John S.; Cristini, Vittorio
2010
Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms. Zbl 1375.35149
Feng, Wenqiang; Salgado, Abner J.; Wang, Cheng; Wise, Steven M.
2017
Error analysis of a mixed finite element method for a Cahn-Hilliard-Hele-Shaw system. Zbl 06695814
Liu, Yuan; Chen, Wenbin; Wang, Cheng; Wise, Steven M.
2017
Global smooth solutions of the three-dimensional modified phase field crystal equation. Zbl 1217.35040
Wang, Cheng; Wise, Steven M.
2010
A second-order energy stable backward differentiation formula method for the epitaxial thin film equation with slope selection. Zbl 1407.76095
Feng, Wenqiang; Wang, Cheng; Wise, Steven M.; Zhang, Zhengru
2018
A uniquely solvable, energy stable numerical scheme for the functionalized Cahn-Hilliard equation and its convergence analysis. Zbl 1398.65208
Feng, Wenqiang; Guan, Zhen; Lowengrub, John; Wang, Cheng; Wise, Steven M.; Chen, Ying
2018
A second order energy stable scheme for the Cahn-Hilliard-Hele-Shaw equations. Zbl 1407.65097
Chen, Wenbin; Feng, Wenqiang; Liu, Yuan; Wang, Cheng; Wise, Steven M.
2019
Adaptive, second-order in time, primitive-variable discontinuous Galerkin schemes for a Cahn-Hilliard equation with a mass source. Zbl 1323.65106
Aristotelous, Andreas C.; Karakashian, Ohannes A.; Wise, Steven M.
2015
Efficient energy stable schemes for isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization. Zbl 1395.65014
Chen, Ying; Lowengrub, John; Shen, Jie; Wang, Cheng; Wise, Steven
2018
Algorithm 801: POLSYS_PLP. A partitioned linear product homotopy code for solving polynomial systems of equations. Zbl 1137.65353
Wise, Steven M.; Sommese, Andrew J.; Watson, Layne T.
2000
Error analysis of a finite difference scheme for the epitaxial thin film model with slope selection with an improved convergence constant. Zbl 1371.35143
Qiao, Zhonghua; Wang, Cheng; Wise, Steven M.; Zhang, Zhengru
2017
Convergence analysis and numerical implementation of a second order numerical scheme for the three-dimensional phase field crystal equation. Zbl 1409.82014
Dong, Lixiu; Feng, Wenqiang; Wang, Cheng; Wise, Steven M.; Zhang, Zhengru
2018
A mass-conservative adaptive FAS multigrid solver for cell-centered finite difference methods on block-structured, locally-Cartesian grids. Zbl 1380.65402
Feng, Wenqiang; Guo, Zhenlin; Lowengrub, John S.; Wise, Steven M.
2018
Mass conservative and energy stable finite difference methods for the quasi-incompressible Navier-Stokes-Cahn-Hilliard system: primitive variable and projection-type schemes. Zbl 1439.76121
Guo, Z.; Lin, P.; Lowengrub, J.; Wise, S. M.
2017
The dynamics of HPV infection and cervical cancer cells. Zbl 1356.92055
Asih, Tri Sri Noor; Lenhart, Suzanne; Wise, Steven; Aryati, Lina; Adi-Kusumo, F.; Hardianti, Mardiah S.; Forde, Jonathan
2016
Convexity splitting in a phase field model for surface diffusion. Zbl 07017833
Backofen, Rainer; Wise, Steven M.; Salvalaglio, Marco; Voigt, Axel
2019
Energy stable numerical schemes for ternary Cahn-Hilliard system. Zbl 1447.65098
Chen, Wenbin; Wang, Cheng; Wang, Shufen; Wang, Xiaoming; Wise, Steven M.
2020
Penalty projection schemes for the Cahn-Hilliard Navier-Stokes diffuse interface model of two phase flow, and their connection to divergence-free coupled schemes. Zbl 1395.35109
Rebholz, Leo G.; Wise, Steven M.; Xiao, Mengying
2018
Global-in-time Gevrey regularity solution for a class of bistable gradient flows. Zbl 1350.35050
Chen, Nan; Wang, Cheng; Wise, Steven
2016
Convergence analysis of the fast subspace descent method for convex optimization problems. Zbl 1442.65426
Chen, Long; Hu, Xiaozhe; Wise, Steven M.
2020
Global-in-time Gevrey regularity solutions for the functionalized Cahn-Hilliard equation. Zbl 1450.35135
Cheng, Kelong; Wang, Cheng; Wise, Steven M.; Yuan, Zixia
2020
An energy stable, hexagonal finite difference scheme for the 2D phase field crystal amplitude equations. Zbl 1349.74360
Guan, Zhen; Heinonen, Vili; Lowengrub, John; Wang, Cheng; Wise, Steven M.
2016
Structure-preserving, energy stable numerical schemes for a liquid thin film coarsening model. Zbl 1468.65119
Zhang, Juan; Wang, Cheng; Wise, Steven M.; Zhang, Zhengru
2021
Discontinuous Galerkin derivative operators with applications to second-order elliptic problems and stability. Zbl 1336.65190
Feng, W.; Lewis, T. L.; Wise, S. M.
2015
An improved error analysis for a second-order numerical scheme for the Cahn-Hilliard equation. Zbl 1459.65141
Guo, Jing; Wang, Cheng; Wise, Steven M.; Yue, Xingye
2021
A weakly nonlinear, energy stable scheme for the strongly anisotropic Cahn-Hilliard equation and its convergence analysis. Zbl 1453.65268
Cheng, Kelong; Wang, Cheng; Wise, Steven M.
2020
Structure-preserving, energy stable numerical schemes for a liquid thin film coarsening model. Zbl 1468.65119
Zhang, Juan; Wang, Cheng; Wise, Steven M.; Zhang, Zhengru
2021
An improved error analysis for a second-order numerical scheme for the Cahn-Hilliard equation. Zbl 1459.65141
Guo, Jing; Wang, Cheng; Wise, Steven M.; Yue, Xingye
2021
Energy stable numerical schemes for ternary Cahn-Hilliard system. Zbl 1447.65098
Chen, Wenbin; Wang, Cheng; Wang, Shufen; Wang, Xiaoming; Wise, Steven M.
2020
Convergence analysis of the fast subspace descent method for convex optimization problems. Zbl 1442.65426
Chen, Long; Hu, Xiaozhe; Wise, Steven M.
2020
Global-in-time Gevrey regularity solutions for the functionalized Cahn-Hilliard equation. Zbl 1450.35135
Cheng, Kelong; Wang, Cheng; Wise, Steven M.; Yuan, Zixia
2020
A weakly nonlinear, energy stable scheme for the strongly anisotropic Cahn-Hilliard equation and its convergence analysis. Zbl 1453.65268
Cheng, Kelong; Wang, Cheng; Wise, Steven M.
2020
An energy stable fourth order finite difference scheme for the Cahn-Hilliard equation. Zbl 1416.65256
Cheng, Kelong; Feng, Wenqiang; Wang, Cheng; Wise, Steven M.
2019
A second order energy stable scheme for the Cahn-Hilliard-Hele-Shaw equations. Zbl 1407.65097
Chen, Wenbin; Feng, Wenqiang; Liu, Yuan; Wang, Cheng; Wise, Steven M.
2019
Convexity splitting in a phase field model for surface diffusion. Zbl 07017833
Backofen, Rainer; Wise, Steven M.; Salvalaglio, Marco; Voigt, Axel
2019
A second-order energy stable backward differentiation formula method for the epitaxial thin film equation with slope selection. Zbl 1407.76095
Feng, Wenqiang; Wang, Cheng; Wise, Steven M.; Zhang, Zhengru
2018
A uniquely solvable, energy stable numerical scheme for the functionalized Cahn-Hilliard equation and its convergence analysis. Zbl 1398.65208
Feng, Wenqiang; Guan, Zhen; Lowengrub, John; Wang, Cheng; Wise, Steven M.; Chen, Ying
2018
Efficient energy stable schemes for isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization. Zbl 1395.65014
Chen, Ying; Lowengrub, John; Shen, Jie; Wang, Cheng; Wise, Steven
2018
Convergence analysis and numerical implementation of a second order numerical scheme for the three-dimensional phase field crystal equation. Zbl 1409.82014
Dong, Lixiu; Feng, Wenqiang; Wang, Cheng; Wise, Steven M.; Zhang, Zhengru
2018
A mass-conservative adaptive FAS multigrid solver for cell-centered finite difference methods on block-structured, locally-Cartesian grids. Zbl 1380.65402
Feng, Wenqiang; Guo, Zhenlin; Lowengrub, John S.; Wise, Steven M.
2018
Penalty projection schemes for the Cahn-Hilliard Navier-Stokes diffuse interface model of two phase flow, and their connection to divergence-free coupled schemes. Zbl 1395.35109
Rebholz, Leo G.; Wise, Steven M.; Xiao, Mengying
2018
Convergence analysis and error estimates for a second order accurate finite element method for the Cahn-Hilliard-Navier-Stokes system. Zbl 06804021
Diegel, Amanda E.; Wang, Cheng; Wang, Xiaoming; Wise, Steven M.
2017
Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms. Zbl 1375.35149
Feng, Wenqiang; Salgado, Abner J.; Wang, Cheng; Wise, Steven M.
2017
Error analysis of a mixed finite element method for a Cahn-Hilliard-Hele-Shaw system. Zbl 06695814
Liu, Yuan; Chen, Wenbin; Wang, Cheng; Wise, Steven M.
2017
Error analysis of a finite difference scheme for the epitaxial thin film model with slope selection with an improved convergence constant. Zbl 1371.35143
Qiao, Zhonghua; Wang, Cheng; Wise, Steven M.; Zhang, Zhengru
2017
Mass conservative and energy stable finite difference methods for the quasi-incompressible Navier-Stokes-Cahn-Hilliard system: primitive variable and projection-type schemes. Zbl 1439.76121
Guo, Z.; Lin, P.; Lowengrub, J.; Wise, S. M.
2017
An $$H^2$$ convergence of a second-order convex-splitting, finite difference scheme for the three-dimensional Cahn-Hilliard equation. Zbl 1338.65221
Guo, Jing; Wang, Cheng; Wise, Steven M.; Yue, Xingye
2016
Stability and convergence of a second-order mixed finite element method for the Cahn-Hilliard equation. Zbl 1433.80005
Diegel, Amanda E.; Wang, Cheng; Wise, Steven M.
2016
Convergence analysis of a fully discrete finite difference scheme for the Cahn-Hilliard-Hele-Shaw equation. Zbl 1342.65174
Chen, Wenbin; Liu, Yuan; Wang, Cheng; Wise, Steven M.
2016
A second-order, weakly energy-stable pseudo-spectral scheme for the Cahn-Hilliard equation and its solution by the homogeneous linear iteration method. Zbl 1375.65137
Cheng, Kelong; Wang, Cheng; Wise, Steven M.; Yue, Xingye
2016
The dynamics of HPV infection and cervical cancer cells. Zbl 1356.92055
Asih, Tri Sri Noor; Lenhart, Suzanne; Wise, Steven; Aryati, Lina; Adi-Kusumo, F.; Hardianti, Mardiah S.; Forde, Jonathan
2016
Global-in-time Gevrey regularity solution for a class of bistable gradient flows. Zbl 1350.35050
Chen, Nan; Wang, Cheng; Wise, Steven
2016
An energy stable, hexagonal finite difference scheme for the 2D phase field crystal amplitude equations. Zbl 1349.74360
Guan, Zhen; Heinonen, Vili; Lowengrub, John; Wang, Cheng; Wise, Steven M.
2016
Analysis of a mixed finite element method for a Cahn-Hilliard-Darcy-Stokes system. Zbl 1330.76065
Diegel, Amanda E.; Feng, Xiaobing H.; Wise, Steven M.
2015
Adaptive, second-order in time, primitive-variable discontinuous Galerkin schemes for a Cahn-Hilliard equation with a mass source. Zbl 1323.65106
Aristotelous, Andreas C.; Karakashian, Ohannes A.; Wise, Steven M.
2015
Discontinuous Galerkin derivative operators with applications to second-order elliptic problems and stability. Zbl 1336.65190
Feng, W.; Lewis, T. L.; Wise, S. M.
2015
Second order convex splitting schemes for periodic nonlocal Cahn-Hilliard and Allen-Cahn equations. Zbl 1349.65298
Guan, Zhen; Lowengrub, John S.; Wang, Cheng; Wise, Steven M.
2014
A linear iteration algorithm for a second-order energy stable scheme for a thin film model without slope selection. Zbl 1305.82034
Chen, Wenbin; Wang, Cheng; Wang, Xiaoming; Wise, Steven M.
2014
A convergent convex splitting scheme for the periodic nonlocal Cahn-Hilliard equation. Zbl 1304.65209
Guan, Zhen; Wang, Cheng; Wise, Steven M.
2014
Convergence analysis of a second order convex splitting scheme for the modified phase field crystal equation. Zbl 1401.82046
Baskaran, A.; Lowengrub, J. S.; Wang, C.; Wise, S. M.
2013
Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation. Zbl 1349.65265
Baskaran, Arvind; Hu, Zhengzheng; Lowengrub, John S.; Wang, Cheng; Wise, Steven M.; Zhou, Peng
2013
An efficient, energy stable scheme for the Cahn-Hilliard-Brinkman system. Zbl 1373.76161
Collins, Craig; Shen, Jie; Wise, Steven M.
2013
A mixed discontinuous Galerkin, convex splitting scheme for a modified Cahn-Hilliard equation and an efficient nonlinear multigrid solver. Zbl 1278.65149
Aristotelous, Andreas C.; Karakashian, Ohannes; Wise, Steven M.
2013
Second-order convex splitting schemes for gradient flows with Ehrlich-Schwoebel type energy: Application to thin film epitaxy. Zbl 1247.65088
Shen, Jie; Wang, Cheng; Wang, Xiaoming; Wise, Steven M.
2012
A linear energy stable scheme for a thin film model without slope selection. Zbl 1326.76007
Chen, Wenbin; Conde, Sidafa; Wang, Cheng; Wang, Xiaoming; Wise, Steven M.
2012
Analysis of a Darcy–Cahn–Hilliard diffuse interface model for the Hele-Shaw flow and its fully discrete finite element approximation. Zbl 1426.76258
Feng, Xiaobing; Wise, Steven
2012
An energy stable and convergent finite-difference scheme for the modified phase field crystal equation. Zbl 1230.82005
Wang, C.; Wise, S. M.
2011
An adaptive multigrid algorithm for simulating solid tumor growth using mixture models. Zbl 1211.65123
Wise, S. M.; Lowengrub, J. S.; Cristini, V.
2011
Nonlinear modelling of cancer: bridging the gap between cells and tumours. Zbl 1181.92046
Lowengrub, J. S.; Frieboes, H. B.; Jin, F.; Chuang, Y-L; Li, X.; Macklin, P.; Wise, S. M.; Cristini, V.
2010
Unconditionally stable finite difference, nonlinear multigrid simulation of the Cahn-Hilliard-Hele-Shaw system of equations. Zbl 1203.76153
Wise, S. M.
2010
Unconditionally stable schemes for equations of thin film epitaxy. Zbl 1201.65166
Wang, Cheng; Wang, Xiaoming; Wise, Steven M.
2010
Three-dimensional multispecies nonlinear tumor growth. II: Tumor invasion and angiogenesis. Zbl 1406.92049
Frieboes, Hermann B.; Jin, Fang; Chuang, Yao-Li; Wise, Steven M.; Lowengrub, John S.; Cristini, Vittorio
2010
Global smooth solutions of the three-dimensional modified phase field crystal equation. Zbl 1217.35040
Wang, Cheng; Wise, Steven M.
2010
An energy-stable and convergent finite-difference scheme for the phase field crystal equation. Zbl 1201.35027
Wise, S. M.; Wang, Cheng; Lowengrub, J. S.
2009
Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation. Zbl 1171.82015
Hu, Z.; Wise, S. M.; Wang, C.; Lowengrub, J. S.
2009
Nonlinear simulations of solid tumor growth using a mixture model: invasion and branching. Zbl 1311.92039
Cristini, Vittorio; Li, Xiangrong; Lowengrub, John S.; Wise, Steven M.
2009
A new phase-field model for strongly anisotropic systems. Zbl 1186.80014
Torabi, Solmaz; Lowengrub, John; Voigt, Axel; Wise, Steven
2009
Three-dimensional multispecies nonlinear tumor growth. I: Model and numerical method. Zbl 1398.92135
Wise, S. M.; Lowengrub, J. S.; Frieboes, H. B.; Cristini, Vittorio
2008
Solving the regularized, strongly anisotropic Cahn-Hilliard equation by an adaptive nonlinear multigrid method. Zbl 1310.82044
Wise, Steven; Kim, Junseok; Lowengrub, John
2007
Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method. Zbl 1334.92214
Zheng, X.; Wise, S. M.; Cristini, V.
2005
Algorithm 801: POLSYS_PLP. A partitioned linear product homotopy code for solving polynomial systems of equations. Zbl 1137.65353
Wise, Steven M.; Sommese, Andrew J.; Watson, Layne T.
2000
all top 5

#### Cited by 1,047 Authors

 42 Yang, Xiaofeng 36 Wang, Cheng 35 Wise, Steven M. 34 Lowengrub, John Samuel 24 Kim, Junseok 20 Miranville, Alain M. 19 Wang, Qi 19 Zhao, Jia 18 Chen, Wenbin 18 Shen, Jie 16 Lee, Hyun Geun 16 Li, Yibao 15 Wang, Xiaoming 14 Qiao, Zhonghua 13 Grasselli, Maurizio 13 Han, Daozhi 12 Shin, Jaemin 11 Gong, Yuezheng 11 Oden, John Tinsley 11 Rocca, Elisabetta 10 Cristini, Vittorio 10 Garcke, Harald 10 Lam, Kei Fong 9 Chaplain, Mark A. J. 9 Cheng, Kelong 9 Du, Qiang 9 Feng, Wenqiang 9 Lee, June-Yub 9 Mei, Liquan 9 Zhang, Zhengru 8 Giorgini, Andrea 8 He, Xiaoming 8 Hu, Bei 8 Kou, Jisheng 8 Li, Xiaoli 8 Perthame, Benoît 8 Signori, Andrea 8 Sun, Shuyu 7 Colli, Pierluigi 7 Dehghan Takht Fooladi, Mehdi 7 Jeong, Darae 7 Li, Xiao 7 van der Zee, Kristoffer George 7 Wu, Hao 7 Yang, Junxiang 6 Byrne, Helen Mary 6 Cheng, Qing 6 Cherfils, Laurence 6 Choi, Yongho 6 Feng, Xinlong 6 Jia, Hongen 6 Ju, Lili 6 Lee, Chaeyoung 6 Lima, Ernesto A. B. F. 6 Lin, Ping 6 Liu, Chun 6 Preziosi, Luigi 6 Sprekels, Jürgen 6 Walker, Shawn W. 6 Wu, Junde 5 Frieboes, Hermann B. 5 Guan, Zhen 5 Guo, Ruihan 5 Guo, Zhenlin 5 Lee, Seunggyu Lee 5 Li, Yukun 5 Liao, HongLin 5 Liu, Zhengguang 5 Macklin, Paul 5 Maini, Philip Kumar 5 Mohammadi, Vahid 5 Nochetto, Ricardo Horacio 5 Promislow, Keith Steven 5 Xu, Yan 5 Yang, Jiang 5 Yue, Xingye 4 Almeida, Regina C. 4 Anderson, Alexander R. A. 4 Bretin, Elie 4 Chen, Chuanjun 4 Chen, Long 4 Colombi, Annachiara 4 Gilardi, Gianni 4 Hao, Wenrui 4 Hawkins-Daarud, Andrea J. 4 Lee, Dongsun 4 Li, Dong 4 Li, Weijia 4 Liu, Yuan 4 Münch, Andreas 4 Scianna, Marco 4 Sommese, Andrew John 4 Tang, Tao 4 Vauchelet, Nicolas 4 Voigt, Axel 4 Wang, Hong 4 Wang, Xiuhua 4 You, Bo 4 Yu, Haijun 4 Zhang, Zhengce ...and 947 more Authors
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#### Cited in 134 Serials

 77 Journal of Computational Physics 58 Journal of Scientific Computing 39 Journal of Theoretical Biology 38 Computer Methods in Applied Mechanics and Engineering 36 Journal of Computational and Applied Mathematics 30 Computers & Mathematics with Applications 26 Applied Numerical Mathematics 24 SIAM Journal on Scientific Computing 23 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 20 Journal of Mathematical Biology 15 SIAM Journal on Numerical Analysis 13 Mathematics of Computation 13 Bulletin of Mathematical Biology 13 Journal of Differential Equations 11 Numerische Mathematik 11 Applied Mathematics Letters 11 Communications in Nonlinear Science and Numerical Simulation 10 Nonlinear Analysis. Real World Applications 9 Mathematical Methods in the Applied Sciences 9 Applied Mathematics and Optimization 9 European Journal of Applied Mathematics 9 Discrete and Continuous Dynamical Systems. Series B 8 Journal of Mathematical Analysis and Applications 8 Advances in Computational Mathematics 8 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 7 Applied Mathematics and Computation 7 Numerical Algorithms 7 Advances in Applied Mathematics and Mechanics 6 Numerical Methods for Partial Differential Equations 5 Nonlinearity 5 Discrete and Continuous Dynamical Systems 5 Mathematical Problems in Engineering 4 Applicable Analysis 4 Mathematics and Computers in Simulation 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 Applied Mathematical Modelling 4 SIAM Journal on Applied Mathematics 4 Engineering Analysis with Boundary Elements 4 Archives of Computational Methods in Engineering 4 Communications on Pure and Applied Analysis 4 Mathematical Biosciences and Engineering 3 SIAM Journal on Mathematical Analysis 3 Computational and Applied Mathematics 3 Mathematical Modelling of Natural Phenomena 3 Discrete and Continuous Dynamical Systems. Series S 3 Journal of Nonlinear Science and Applications 3 Science China. Mathematics 3 East Asian Journal on Applied Mathematics 2 Archive for Rational Mechanics and Analysis 2 Journal of Engineering Mathematics 2 Mathematical Biosciences 2 Physica A 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Chaos, Solitons and Fractals 2 BIT 2 International Journal for Numerical Methods in Engineering 2 SIAM Journal on Control and Optimization 2 Chinese Annals of Mathematics. Series B 2 Mathematical and Computer Modelling 2 Asymptotic Analysis 2 Applications of Mathematics 2 SIAM Review 2 Journal of Nonlinear Science 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Journal of Mathematical Fluid Mechanics 2 Interfaces and Free Boundaries 2 Computational Geosciences 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Multiscale Modeling & Simulation 2 Electronic Research Archive 1 International Journal of Engineering Science 1 International Journal for Numerical Methods in Fluids 1 Journal of Fluid Mechanics 1 Physics Reports 1 Rocky Mountain Journal of Mathematics 1 Calcolo 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Functional Analysis 1 Osaka Journal of Mathematics 1 Quarterly of Applied Mathematics 1 Applied Mathematics and Mechanics. (English Edition) 1 Bulletin of the Iranian Mathematical Society 1 Computational Mechanics 1 Computational Mathematics and Modeling 1 Japan Journal of Industrial and Applied Mathematics 1 Communications in Partial Differential Equations 1 Journal of Statistical Computation and Simulation 1 Linear Algebra and its Applications 1 Journal of Dynamics and Differential Equations 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Continuum Mechanics and Thermodynamics 1 Applied Mathematics. Series B (English Edition) 1 Calculus of Variations and Partial Differential Equations 1 Journal of Inverse and Ill-Posed Problems 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Mechanism and Machine Theory 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Discrete Dynamics in Nature and Society ...and 34 more Serials
all top 5

#### Cited in 36 Fields

 443 Partial differential equations (35-XX) 426 Numerical analysis (65-XX) 230 Biology and other natural sciences (92-XX) 185 Fluid mechanics (76-XX) 88 Statistical mechanics, structure of matter (82-XX) 72 Mechanics of deformable solids (74-XX) 36 Calculus of variations and optimal control; optimization (49-XX) 28 Classical thermodynamics, heat transfer (80-XX) 11 Dynamical systems and ergodic theory (37-XX) 10 Integral equations (45-XX) 9 Probability theory and stochastic processes (60-XX) 8 Statistics (62-XX) 8 Computer science (68-XX) 8 Optics, electromagnetic theory (78-XX) 6 Real functions (26-XX) 6 Ordinary differential equations (34-XX) 4 Approximations and expansions (41-XX) 4 Operator theory (47-XX) 4 Mechanics of particles and systems (70-XX) 2 General and overarching topics; collections (00-XX) 2 Commutative algebra (13-XX) 2 Algebraic geometry (14-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Quantum theory (81-XX) 2 Information and communication theory, circuits (94-XX) 1 History and biography (01-XX) 1 Potential theory (31-XX) 1 Functional analysis (46-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX) 1 Mathematics education (97-XX)