Steven M. Wise

Professor of Mathematics at the University of Tennessee

About Research Publications Projects Teaching CV Classical Numerical Analysis

Publications | Steven M. Wise

Publications

Book

Abner J. Salgado and Steven M. Wise, Classical Numerical Analysis: A Comprehensive Course, Cambridge University Press (2023). (doi: 10.1017/9781108942607)

Published Papers

Preprints

  1. E. Habbershaw, C.D. Hauck, and S.M. Wise, Implicit Update of the Moment Equations for a Multi-Species, Homogeneous BGK Model. (arXiv: abs/2404.18039)

  2. T. Luong and S.M. Wise, A Nonnegative Weak Solution to the Phase Field Crystal Model with Degenerate Mobility. (arXiv: abs/2404.13482)

  3. Y. Sun, J. Wu, M. Jiang, S.M. Wise, and Z. Guo, A Thermodynamically Consistent Phase-Field Model and an Entropy Stable Numerical Method for Simulating Two-Phase Flows with Thermocapillary Effects. (arXiv: abs/2404.04950)

  4. A.E. Diegel, C. Wang, and S.M. Wise, Convergence Analysis of a Preconditioned Steepest Descent Solver for the Cahn-Hilliard Equation with Logarithmic Potential. (arXiv: abs/2401.16316)

  5. E. Habbershaw, R.S. Glasby, J.R. Haack, C.D. Hauck, and S.M. Wise, Asymptotic Relaxation of Moment Equations for a Multi-species, Homogeneous BGK Model. (arXiv: abs/2310.12885)

  6. Y. Guo, C. Wang, S.M. Wise, Z. Zhang, Convergence Analysis of a Positivity-Preserving Numerical Scheme for the Cahn-Hilliard-Stokes System with Flory-Huggins Energy Potential. (arXiv: abs/2303.11609)

  7. A. Christlieb, K. Promislow, Z. Tan, S. Wang, B. Wetton,S.M. Wise, Benchmark Computation of Morphological Complexity in the Functionalized Cahn-Hilliard Gradient Flow. (arXiv: abs/2006.04784)

2024

  1. E. Habbershaw and S.M. Wise, Year-2 Progress Report on Numerical Methods for BGK-Type Kinetic Equations, TRACE: Faculty Publications and Other Works, The University of Tennessee, Mathematics Report Number 11 (2024) (129 pages). (Trace: Math Faculty Report 11)

  2. C. Wang, J. Wang, S.M. Wise, Z. Xia, and L. Xu, Convergence Analysis of a Temporally Second-Order Accurate Finite Element scheme for the Cahn-Hilliard-Magnetohydrodynamics System of Equations, J. Comput. Appl. Math. 436 (2024) 115409 (17 pages). (doi: 10.1016/j.cam.2023.115409)

2023

  1. Shibin Dai, Joseph Renzi, and S.M. Wise, Gamma Convergence of the DeGennes-Cahn-Hilliard Energy, Comm. Math. Sci. 21 (2023) 2131-2144. (doi: 10.4310/CMS.2023.v21.n8.a3)

  2. C. Liu, C. Wang, S.M. Wise, X. Yue, and S. Zhou, A Second Order Accurate, Positivity Preserving Numerical Method for the Poisson-Nernst-Planck System and Its Convergence Analysis, J. Sci. Comput. 97 (2023) 23 (35 pages). (doi: 10.1007/s10915-023-02345-9)

  3. X. Tang, S. Li, J.S. Lowengrub, and S.M. Wise, Phase Field Modeling and Computation of Vesicle Growth or Shrinkage, J. Math. Biol. 86 (2023) 97 (31 pages). (doi: 10.1007/s00285-023-01928-2)

  4. K. Cheng, C. Wang, and S.M. Wise, High Order Accurate and Convergent Numerical Scheme for the Strongly Anisotropic Cahn-Hilliard Model, Numer. Methods Partial Diff. Eq. (2023) (23 pages). (doi: 10.1002/num.23034)

  5. M. Punke, S.M. Wise, A. Voigt, and M. Salvalaglio, Improved Time Integration for Phase-Field Crystal Models of Solidification, Proc. Appl. Math. Mech. 23 (2023) e202200112 (6 pages). (doi: 10.1002/pamm.202200112)

  6. K. Cheng, C. Wang, and S.M. Wise, An Energy Stable Finite Difference Scheme for the Ericksen-Leslie System with Penalty Function and its Optimal Rate Convergence Analysis, Commun. Math. Sci. 21 (2023) 1135–1169. (doi: 10.4310/CMS.2023.v21.n4.a10)

  7. J.H. Park, A.J. Salgado, and S.M. Wise, Benchmark Computations of the Phase Field Crystal and Functionalized Cahn-Hilliard Equations via Fully Implicit, Nesterov Accelerated Schemes, Commun. Comput. Phys. 33 (2023) 367–398. (doi: 10.4208/cicp.OA-2022-0117)

2022

  1. X. Chen, C. Wang, and S.M. Wise, A Preconditioned Steepest Descent Solver for the Cahn-Hilliard Equation with Variable Mobility, Int. J. Numer. Anal. Model. 19 (2022) 839–863. (pdf: IJNAM)

  2. C. Wang and S.M. Wise, A Thermodynamically-Consistent Phase Field Crystal Model of Solidification with Heat Flux, J. Math. Study 55 (2022) 1–21. (doi: 10.4208/jms.v55n4.22.01)

  3. M. Punke, S.M. Wise, A. Voigt, and M. Salvalaglio, Explicit Temperature Coupling in Phase-Field Crystal Models of Solidification, 30 (2022) 074004 (18 pages). (doi: 10.1088/1361-651X/ac8abd)

  4. M. Yuan, W. Chen, C. Wang, S.M. Wise, and Z. Zhang, A Second Order Accurate in Time, Energy Stable Finite Element Scheme for the Flory-Huggins-Cahn-Hilliard Equation, Adv. Appl. Math. Mech. 14 (2022) 1477–1508. (doi: 10.4208/aamm.OA-2021-0331)

  5. E. Habbershaw and S.M. Wise, A Progress Report on Numerical Methods for BGK-Type Kinetic Equations, TRACE: Faculty Publications and Other Works, The University of Tennessee, Mathematics Report Number 10 (2022) (81 pages). (Trace: Math Faculty Report 10)

  6. L. Dong, C. Wang, S.M. Wise, and Z. Zhang, Optimal Rate Convergence Analysis of a Numerical Scheme for the Ternary Cahn-Hilliard System with a Flory-Huggins-deGennes Energy Potential, J. Comp. Appl. Math. 415 (2022) 114474 (18 pages). (doi: 10.1016/j.cam.2022.114474)

  7. K. Cheng, C. Wang, S.M. Wise, and Y. Wu, A Third Order Accurate in Time, BDF-Type Energy Stable Scheme for the Cahn-Hilliard Equation, Numer. Math. Theor. Meth. Appl. 15 (2022) 279–303. (doi: 10.4208/nmtma.OA-2021-0165)

  8. C. Liu, C. Wang, Y. Wang, and S.M. Wise, Convergence Analysis of the Variational Operator Splitting Scheme for a Reaction-Diffusion System with Detailed Balance, SIAM J. Numer. Anal. 60 (2022) 781–803. (doi: 10.1137/21M1421283)

  9. C. Liu, C. Wang, S.M. Wise, X. Yue, and S. Zhou, An Iterative Solver for the Poisson-Nernst-Planck System and its Convergence Analysis, J. Comput. Appl. Math 406 (2022) 114017 (13 pages). (doi: 10.1016/j.cam.2021.114017)

  10. W. Chen, J. Jing, C. Wang, X. Wang and S.M. Wise, A Modified Crank-Nicolson Numerical Scheme for the Flory-Huggins Cahn-Hilliard Model, Commun. Comput. Phys. 31 (2022) 60–93. (doi: 10.4208/cicp.OA-2021-0074)

2021

  1. J. Park, A.J. Salgado, and S.M. Wise, Preconditioned Accelerated Gradient Descent Methods for Locally Lipschitz Smooth Objectives with Applications to the Solution of Nonlinear PDEs, J. Sci. Comput. 89 (2021) 17 (37 pages). (doi: 10.1007/s10915-021-01615-8)

  2. S. Sahyoun, D. Wilson, S.M. Djouadi, S.M. Wise, H.A. Abderrahmane, Proper Orthogonal Decomposition Reduced Order Model for Tear Film Flows, American Control Conference (ACC) (2021) 2763–2768. (doi: 10.23919/ACC50511.2021.9483018)

  3. C. Liu, C. Wang, S.M. Wise, X. Yue, and S. Zhou, A Positivity-Preserving, Energy Stable and Convergent Numerical Scheme for the Poisson-Nernst-Planck System, Math. Comp. 90 (2021) 2071–2106. (doi: 10.1090/mcom/3642)

  4. L. Dong, C. Wang, S.M. Wise, and Z. Zhang, A Positivity-Preserving, Energy Stable Scheme for a Ternary Cahn-Hilliard System with Singular Interfacial Parameters, J. Comput. Phys. 442 (2021) 110451 (29 pages). (doi: 10.1016/j.jcp.2021.110451)

  5. J. Zhang, C. Wang, S.M. Wise, and Z. Zhang, Structure-preserving, Energy Stable Numerical Schemes for a Liquid Thin Film Coarsening Model, SIAM J. Sci. Comput. 42 (2021) A1248–A1272. (doi: 10.1137/20M1375656)

  6. M. Yuan, W. Chen, C. Wang, S.M. Wise, and Z. Zhang, An Energy Stable Finite Element Scheme for the Three-Component Cahn-Hilliard-Type Model for Macromolecular Microsphere Composite Hydrogels, J. Sci. Comp. 87 (2021) 78.(doi: 10.1007/s10915-021-01508-w)

  7. M. Salvalaglio, M. Selch, A. Voigt, and S.M. Wise, Doubly Degenerate Diffuse Interface Models of Anisotropic Surface Diffusion, Math. Methods Appl. Sci. 44 (2021) 5406–5417. (doi: 10.1002/mma.7118)

  8. M. Salvalaglio, A. Voigt, and S.M. Wise, Doubly Degenerate Diffuse Interface Models of Surface Diffusion, Math. Methods Appl. Sci. 44 (2021) 5385–5405. (doi: 10.1002/mma.7116)

  9. J. Guo, C. Wang, S.M. Wise and X. Yue, An Improved Error Analysis for a Second-Order Numerical Scheme for the Cahn-Hilliard Equation, J. Comput. Appl. Math. 388 (2021). 113300. (doi: 10.1016/j.cam.2020.113300)

  10. Z. Guo, F. Yu, P. Lin, S.M. Wise, and J.S. Lowengrub, A Diffuse Domain Method for Two Phase Flows with Large Density Ratio in Complex Geometries, J. Fluid Mech. 907 (2021) A38. (doi: 10.1017/jfm/jfm.2020.790)

2020

  1. C. Zhang, J. Ouyang, C. Wang, and S.M. Wise, Numerical Comparison of Modified-Energy Stable SAV-Type Schemes and Classical BDF Methods on Benchmark Problems for the Functionalized Cahn-Hilliard Equation, J. Comput. Phys. 423 (2020) 109772 (35 pages). (doi: 10.1016/j.jcp.2020.109772)

  2. W. Chen, C. Wang, S. Wang, X. Wang, and S.M. Wise, Energy Stable Numerical Schemes for a Ternary Cahn-Hilliard System, J. Sci. Comp. 84 (2020) 27 (36 pages). (doi: 10.1007/s10915-020-01276-z)

  3. L. Chen, X. Hu, and S.M. Wise, Convergence Analysis of the Fast Subspace Descent Methods for Convex Optimization Problems, Math. Comp. 89, (2020) 2249–2282. (doi: 10.1090/mcom/3526)

  4. K. Cheng, C. Wang, and S.M. Wise, A Weakly Nonlinear, Energy Stable Scheme for the Strongly Anisotropic Cahn-Hilliard Equation and Its Convergence Analysis, J. Comput. Phys. 405 (2020) 109109 (28 pages). (doi: 10.1016/j.jcp.2019.109109)

  5. K. Cheng, C. Wang, S.M. Wise, and Z. Yuan, Global-in-Time Gevrey Regularity Solutions for the Functionalized Cahn-Hilliard Equation, Discrete Cont. Dyn. Syst. Ser. S 13 (2020) 2211–2229. (doi: 10.3934/dcdss.2020186)

2019

  1. K. Cheng, C. Wang, and S.M. Wise, An Energy Stable BDF2 Fourier Pseudo-Spectral Numerical Scheme for the Square Phase Field Crystal Equation, Commun. Comput. Phys. 26 (2019) 1335–1364. (doi: 10.4208/cicp.2019.js60.10)

  2. J.M. Church, Z. Guo, P.K. Jimack, A. Madzvamuse, K. Promislow, B. Wetton, S.M. Wise, and F. Yang, {High Accuracy Benchmark Problems for Allen-Cahn and Cahn-Hilliard Dynamics, Commun. Comput. Phys. 26 (2019), pp. 947–972. (doi: 10.4208/cicp.OA-2019-0006)

  3. W. Chen, C. Wang, X. Wang, and S.M. Wise, Positivity-Preserving, Energy Stable Numerical Schemes for the Cahn-Hilliard Equation with Logarithmic Potential, J. Comput. Phys. X 3 (2019) 100031 (29 pages). (doi: 10.1016/j.jcpx.2019.100031)

  4. K. Cheng, W. Feng, C. Wang, and S.M. Wise, An Energy Stable Fourth Order Finite Difference Scheme for the Cahn-Hilliard Equation, J. Comput. Appl. Math. 362 (2019) 574–595. (doi: 10.1016/j.cam.2018.05.039)

  5. W. Chen, W. Feng, Y. Liu, C. Wang, and S.M. Wise, A Second Order Energy Stable Scheme for the Cahn-Hilliard-Hele-Shaw Equations, Discrete Cont. Dyn. Syst. Ser. B 24 (2019) 149–182. (doi: 10.3934/dcdsb.2018090)

  6. R. Backofen, S.M. Wise, M. Salvalaglio, and A. Voigt, Convexity Splitting in a Phase Field Model for Surface Diffusion, Int. J. Numer. Anal. Model. 16 (2019) 192–209. (pdf: IJNAM)

2018

  1. W. Feng, C. Wang, S.M. Wise, Z. Zhang, A Second-Order Energy Stable Backward Differentiation Formula Method for the Epitaxial Thin Film Equation with Slope Selection, Numer. Methods Partial Differ. Eq. 34 (2018) 1975–2007. (doi: 10.1002/num.22271)

  2. W. Feng, Z. Guan, J.S. Lowengrub, C. Wang, S.M. Wise, and Y. Chen, An Energy Stable Finite-Difference Scheme for the Functionalized Cahn-Hilliard Equation and its Convergence Analysis, J. Sci. Comput. 76 (2018) 1938–1967. (doi: 10.1007/s10915-018-0690-1)

  3. Y. Chen, J.S. Lowengrub, J. Shen, C. Wang, and S.M. Wise, Efficient Energy Stable Schemes for Isotropic and Strongly Anisotropic Cahn-Hilliard Systems with the Willmore Regularization, J. Comput. Phys. 365 (2018) 56–73. (doi: 10.1016/j.jcp.2018.03.024)

  4. L.G. Rebholz, S.M. Wise, and M. Xiao, Penalty-Projection Schemes for the Cahn-Hilliard Navier-Stokes Diffuse Interface Model of Two Phase Flow, and their Connection to Divergence-Free Coupled Schemes, Int. J. Numer. Anal. Model. 15 (2018) 649–676. (pdf: IJNAM)

  5. J. Cummings, J.S. Lowengrub, B.G. Sumpter, S.M. Wise, and R. Kumar, Modeling Solvent Evaporation During Thin Film Formation in Phase Separating Polymer Mixtures, Soft Matter 14 (2018) 1833–1846. (doi: 10.1039/c7sm02560b)

  6. L. Dong, W. Feng, C. Wang, S.M. Wise, and Z. Zhang, Convergence Analysis and Numerical Implementation of a Second Order Numerical Scheme for the Three-Dimensional Phase Field Crystal Equation, Comput. Math. Appl. 75 (2018) 1912–1928. (doi: 10.1016/j.camwa.2017.07.012)

  7. Y. Yan, W. Chen, C. Wang, and S.M. Wise, A Second-Order Energy Stable BDF Numerical Scheme for the Cahn-Hilliard Equation, Commun. Comput. Phys. 23 (2018) 572–602. (doi: 10.4208/cicp.OA-2016-0197)

  8. W. Feng, Z. Guo, J.S. Lowengrub, and S.M. Wise, A Mass-Conservative Adaptive FAS Multigrid Solver for Cell-Centered Finite Difference Methods on Block-Structured, Locally-Cartesian Grids, J. Comput. Phys. 352 (2018) 463–497. (doi: 10.1016/j.jcp.2017.09.065)

2017

  1. A. Diegel, C. Wang, X. Wang, and S.M. Wise, Error Analysis of a Second Order Mixed Finite Element Method for the Cahn-Hilliard-Navier-Stokes Equation, Numer. Math. 137 (2017) 495–534. (doi: 10.1007/s00211-017-0887-5)

  2. Z. Guo, P. Lin, J.S. Lowengrub, and S.M. Wise, Mass Conservative and Energy Stable Finite Difference Methods for the Quasi-Incompressible Navier-Stokes-Cahn-Hilliard System: Primitive Variable and Projection-Type Schemes, Comput. Methods Appl. Mech. Engrg. 326 (2017) 144–174. (doi: 10.1016/j.cma.2017.08.011)

  3. Z. Qiao, C. Wang, S.M. Wise, and Z. Zhang, Error Analysis of an Energy Stable Finite Difference Scheme for the Epitaxial Thin Film Model with Slope Selection with an Improved Convergence Constant, Int. J. Numer. Anal. Model. 14 (2017) 283–305. (pdf: IJNAM)

  4. Y. Liu, W. Chen, C. Wang, and S.M. Wise, Error Analysis of a Mixed Finite Element Method for a Cahn-Hilliard-Hele-Shaw System, Numer. Math. 135 (2017) 679–709. (doi: 10.1007/s00211-016-0813-2)

  5. W. Feng, A.J. Salgado, C. Wang, S.M. Wise, Preconditioned Steepest Descent Methods for some Nonlinear Elliptic Equations Involving p-Laplacian Terms, J. Comput. Phys. 334 (2017) 45–67. (doi: 10.1016/j.jcp.2016.12.046)

2016

  1. K. Cheng, C. Wang, S.M. Wise, and Y. Yue, A Second-Order, Weakly Energy-Stable Pseudo-Spectral Scheme for the Cahn-Hilliard Equation and its Solution by the Homogeneous Linear Iteration Method, J. Sci. Comput. 69 (2016) 1083–1114. (doi: 10.1007/s10915-016-0228-3)

  2. A. Diegel, C. Wang, and S.M. Wise, Stability and Convergence of a Second Order Mixed Finite Element Method for the Cahn-Hilliard Equation, IMA J. Numer. Anal. 36 (2016) 1867–1897. (doi: 10.1093/imanum/drv065)

  3. Z. Guan, V. Heinonen, J.S. Lowengrub, C. Wang, and S.M. Wise, An Energy Stable, Hexagonal Finite Difference Scheme for the 2D Phase Field Crystal Amplitude Equations, J. Comput. Phys. 321 (2016) 1026–1054. (doi: 10.1016/j.jcp.2016.06.007)

  4. N. Chen, C. Wang, and S.M. Wise, Global-in-time Gevrey Regularity Solution for a Class of Bistable Gradient Flows, Discrete Cont. Dyn. Syst. Ser. B 21 (2016) 1689–1711. (doi: 10.3934/dcdsb.2016018)

  5. W. Chen, Y. Liu, C. Wang, and S.M. Wise, An Optimal-Rate Convergence Analysis of a Fully Discrete Finite Difference Scheme for the Cahn-Hilliard-Hele-Shaw Equation, Math. Comp. 85 (2016) 2231–2257. (doi: 10.1090/mcom3052)

  6. Tri Sri Noor Asih, Suzanne Lenhart, S.M. Wise, Lina Aryati, F. Adi-Kusumo, Mardiah S. Hardianti, and Jonathan Forde, The Dynamics of HPV Infection and Cervical Cancer Cells, Bull. Math. Biol. 78 (2016) 4–20. (doi: 10.1007/s11538-015-0124-2)

  7. J. Guo, C. Wang, S.M. Wise, and X. Yue, An $H^2$ Convergence of a Second-Order Convex-Splitting, Finite Difference Scheme for the Three-Dimensional Cahn-Hilliard Equation, Commun. Math. Sci. 14 (2016) 489–515. (doi: 10.4310/CMS.2016.v14.n2.a8)

2015

  1. W. Feng, T. Lewis, and S.M. Wise, Discontinuous Galerkin Derivative Operators with Applications to Second Order Elliptic Problems and Stability, Math. Methods Appl. Sci. 38 (2015) 5160–5182. (doi: 10.1002/mma.3440)

  2. A. Aristotelous, O. Karakashian, and S.M. Wise, Second-Order in Time, Primitive-Variable Discontinuous Galerkin Schemes for a Cahn-Hilliard Equation with a Mass Source Term, IMA J. Numer. Anal. 35 (2015) 1167–1198. (doi: 10.1093/imanum/dru035)

  3. A. Diegel, X. Feng, and S.M. Wise, Analysis of a Mixed Finite Element Method for a Cahn-Hilliard-Darcy-Stokes System, SIAM J. Numer. Anal. 53 (2015) 127–152. (doi: 10.1137/130950628)

2014

  1. Z. Guan, C. Wang, and S.M. Wise, A Convergent Convex Splitting Scheme for the Periodic Nonlocal Cahn-Hilliard Equation, Numer. Math. 128 (2014) 377–406. (doi: 10.1007/s00211-014-0608-2)

  2. Z. Guan, J.S. Lowengrub, C. Wang, and S.M. Wise, Second-Order Convex Splitting Schemes for Non-local Cahn-Hilliard and Allen-Cahn Equations, J. Comput. Phys. 277 (2014) 48–71. (doi: 10.1016/j.jcp.2014.08.001)

  3. Y. Chen, S.M. Wise, V.B. Shenoy, and J.S. Lowengrub, A Stable Scheme for a Nonlinear, Multispecies Tumor Growth Model with an Elastic Membrane, Int. J. Numer. Meth. Biomed. Engng. 30 (2014) 726–754. (doi: 10.1002/cnm.2624)

  4. W. Chen, C. Wang, X. Wang, and S.M. Wise, A Linear Iteration Algorithm for an Energy Stable Second Order Scheme for a Thin Film Model Without Slope Selection, J. Sci. Comput. 59 (2014) 574–601. (doi: 10.1007/s10915-013-9774-0)

2013

  1. A. Baskaran, J.S. Lowengrub, C. Wang, and S.M. Wise, Convergence of a Second Order Convex Splitting Scheme for the Modified Phase Field Crystal Equation, SIAM J. Numer. Anal. 51 (2013) 2851–2873. (doi: 10.1137/120880677)

  2. A. Aristotelous, O. Karakashian, S.M. Wise, A Mixed Discontinuous Galerkin, Convex Splitting Scheme for a Modified Cahn-Hilliard Equation and an Efficient Nonlinear Multigrid Solver, Discrete Cont. Dyn. Syst. B 18 (2013) 2211–2238. (doi: 10.3934/dcdsb.2013.18.2211)

  3. A. Baskaran, Z. Hu, J.S. Lowengrub, C. Wang, S.M. Wise, and P. Zhou, Energy Stable and Efficient Finite-Difference Nonlinear-Multigrid Schemes for the Modified Phase Field Crystal Equation, J. Comput. Phys. 250 (2013) 270–292. (doi: 10.1016/j.jcp.2013.04.024)

  4. C. Collins, J. Shen, and S.M. Wise, An Efficient, Energy Stable Scheme for the Cahn-Hilliard-Brinkman System, Commun. Comput. Phys. 13 (2013) 929–957. (doi: 10.4208/cicp.171211.130412a)

2012

  1. W. Chen, S. Conde, C. Wang, X. Wang, and S.M. Wise, A Linear Energy Stable Scheme for a Thin Film Model without Slope Selection, J. Sci. Comput. 52 (2012) 546–562. (doi: 10.1007/s10915-011-9559-2)

  2. P. Zhou, S.M. Wise, X. Li, and J.S. Lowengrub, Coarsening of Elastically Stressed, Strongly Anisotropic Driven Thin Films, Phys. Rev. E 85 (2012) 061605. (doi: 10.1103/PhysRevE.85.061605)

  3. X. Feng and S.M. Wise, Analysis of a Darcy-Cahn-Hilliard Diffuse Interface Model for the Hele-Shaw Flow and its Fully Discrete Finite Element Approximation, SIAM J. Numer. Anal. 50 (2012) 1320–1343. (doi: 10.1137/110827119)

  4. J. Shen, C. Wang, X. Wang, and S.M. Wise, Second-Order Convex Splitting Schemes for Gradient Flows with Ehrlich-Schwoebel Type Energy: Application to Thin Film Epitaxy, SIAM J. Numer. Anal. 50 (2012) 105–125. (doi: 10.1137/110822839)

  5. Z. Hu, J.S. Lowengrub, S.M. Wise, and A. Voigt, Phase-Field Modeling of Epitaxial Growth: Applications to Step Trains and Island Dynamics, Physica D 241 (2012) 77–94. (doi: 10.1016/j.physd.2011.09.004)

2011

  1. C. Wang and S.M. Wise, An Energy Stable and Convergent Finite Difference Scheme for the Modified Phase Field Crystal Equation, SIAM J. Numer. Anal. 49 (2011) 945–969. (doi: 10.1137/090752675)

  2. S.M. Wise, J.S. Lowengrub, and V. Cristini, An Adaptive Algorithm for Simulating Solid Tumor Growth using Mixture Models, Math. Comput. Model. 53 (2011) 1–20. (doi: 10.1016/j.mcm.2010.07.007)

2010

  1. C. Wang and S.M. Wise, Global Smooth Solutions of the Three-Dimensional Modified Phase Field Crystal Equation, Methods Appl. Anal. 17 (2010) 191–212. (doi: 10.4310/MAA.2010.v17.n2.a4)

  2. Y.L. Chuang, F. Jin, and S.M. Wise, Numerical Schemes, in V. Cristini and J.S. Lowengrub (Authors), Multiscale Modeling of Cancer: An Integrated Experimental and Mathematical Modeling Approach, Cambridge University Press (2010) 153–182. (doi: 10.1017/CBO9780511781452.009)

  3. H.B. Frieboes, F. Jin, Y.L. Chuang, S.M. Wise, J.S. Lowengrub, and V. Cristini, Three-Dimensional Multispecies Nonlinear Tumor Growth–II: Angiogenesis and Tissue Invasion, J. Theor. Biol. 264 (2010) 1254–1278. (doi: 10.1016/j.jtbi.2010.02.036)

  4. S.M. Wise, Unconditionally Stable Finite Difference, Nonlinear Multigrid Simulation of the Cahn-Hilliard-Hele-Shaw System of Equations, J. Sci. Comput. 44 (2010) 38–68. (doi: 10.1007/s10915-010-9363-4)

  5. C. Wang, X. Wang, and S.M. Wise, Unconditionally Stable Schemes for Equations of Thin Film Epitaxy, Discrete Contin. Dyn. Syst. Ser. A 28 (2010) 405–423. (doi: 10.3934/dcds.2010.28.405)

  6. J.S. Lowengrub, H.B. Frieboes, F. Jin, Y.L. Chuang, X. Li, P. Macklin, S.M. Wise, and V. Cristini, Nonlinear Modeling of Cancer: Bridging the Gap Between Cells and Tumors, Nonlinearity 23 (2010) R1–R91. (doi: 10.1088/0951-7715/23/1/R01)

2009

  1. P. Zhou, J.S. Lowengrub, and S.M. Wise, Coarsening of 3D Thin Films Under the Influence of Strong Surface Anisotropy and Elastic Stresses, TMS 2009 (138th annual meeting), Supplemental Proceedings: Materials Characterization, Computation and Modeling (2009) 39–46.

  2. Z. Hu, S.M. Wise, C. Wang, and J.S. Lowengrub, Stable Finite Difference, Nonlinear Multigrid Simulation of the Phase Field Crystal Equation, J. Comput. Phys. 228 (2009) 5323–5339. (doi: 10.1016/j.jcp.2009.04.020)

  3. S.M. Wise, C. Wang, and J.S. Lowengrub, An Energy Stable and Convergent Finite Difference Scheme for the Phase Field Crystal Equation, SIAM J. Numer. Anal. 47 (2009) 2269–2288. (doi: 10.1137/080738143)

  4. J.S. Lowengrub, V. Cristini, H.B. Frieboes, X. Li, P. Macklin, S. Sanga, S.M. Wise, and X. Zheng, Lecture Notes on Nonlinear Tumor Growth: Modeling and Simulation, in B.C. Khoo, Z. Li, and P. Lin (Editors) Interface Problems and Methods in Biological and Physical Flows, World Scientific (2009) 69–133. (doi: 10.1142/9789812837851_0002)

  5. E.L. Bearer, J.S. Lowengrub, H.B. Frieboes, Y.L. Chuang, F. Jin, S.M. Wise, M. Ferrari, D.B. Agus, and V. Cristini, Multiparameter Computational Modeling of Tumor Invasion, Cancer Res. 69 (2009) 4493–4501. (doi: 10.1158/0008-5472.CAN-08-3834)

  6. S. Torabi, J.S. Lowengrub, A. Voigt, and S.M. Wise, A New Phase-Field Model for Strongly Anisotropic Systems, Proc. R. Soc. A 465 (2009) 1337–1359. (doi: 10.1098/rspa.2008.0385)

  7. V. Cristini, X. Li, J.S. Lowengrub, and S.M. Wise, Nonlinear Simulations of Solid Tumor Growth using a Mixture Model: Invasion and Branching, J. Math. Biol. 58 (2009) 723–763. (doi: 10.1007/s00285-008-0215-x)

2008

  1. S.M. Wise, J.S. Lowengrub, H.B. Frieboes, and V. Cristini, Three-Dimensional Multispecies Nonlinear Tumor Growth–I: Model and Numerical Method, J. Theor. Biol. 253 (2008) 524–543. (doi: 10.1016/j.jtbi.2008.03.027)

  2. S. Torabi, S.M. Wise, S. Li, A. Voigt, J.S. Lowengrub, and P. Zhou, Simulations of Nonlinear Strongly Anisotropic, Misfitting Crystals and Thin Films, MRS Proceedings 1087 (2008) 1087-V02-01. (doi: 10.1557/PROC-1087-V02-01)

  3. V. Cristini, H.B. Frieboes, X. Li, J.S. Lowengrub, P. Macklin, S. Sanga, S.M. Wise, and X. Zheng, Nonlinear Modeling and Simulation of Tumor Growth, in N. Bellomo, M. Chaplain, and E. De Angelis (Editors), Selected Topics in Cancer Modeling: Genesis, Evolution, Immune Competition, and Therapy, Birkhauser (2008) 1–69. (doi: 10.1007/978-0-8176-4713-1_6)

  4. Z. Hu, S. Li, J.S. Lowengrub, S.M. Wise, and A. Voigt, Phase Field Modeling of Nanoscale Island Dynamics, TMS 2008 (137th annual meeting) Supplemental Proceedings: Materials Processing and Properties (2008) 111–116.

2007

  1. S. Torabi, S.M. Wise, J.S. Lowengrub, A. Ratz, and A. Voigt, A New Method for Simulating Strongly Anisotropic Cahn-Hilliard Equations, MS&T 2007 Conference Proceedings (2007) 1432–1444.

  2. S.M. Wise, J.S. Kim, and J.S. Lowengrub, Solving the Regularized, Strongly Anisotropic Cahn-Hilliard Equation by an Adaptive Nonlinear Multigrid Method, J. Comput. Phys. 226 (2007) 414–446. (doi: 10.1016/j.jcp.2007.04.020)

  3. H.B. Frieboes, J.S. Lowengrub, S.M. Wise, X. Zheng, P. Macklin, E.L. Bearer, and V. Cristini, Computer Simulation of Glioma Growth and Morphology, NeuroImage 37 (2007) S59–S70. (doi: 10.1016/j.neuroimage.2007.03.008)

1996 – 2006

  1. J. Favergeon, J.Y. Huh, W.C. Johnson, and S.M. Wise, Wetting Transitions in a Binary Thin Film, Met. Mater. Int. 11 (2005) 487–497. (doi: 10.1007/BF03027499)

  2. S.M. Wise, J.S. Lowengrub, J.S. Kim, K. Thornton, P. Voorhees, and W.C. Johnson, Quantum Dot Formation on a Strain-Patterned Epitaxial Thin Film, Appl. Phys. Lettr. 87 (2005) 133102. (doi: 10.1063/1.2061852)

  3. X. Zheng, S.M. Wise, and V. Cristini, Nonlinear Simulation of Tumor Necrosis, Neo-Vascularization and Tissue Invasion via an Adaptive Finite-Element/Level-Set Method, Bull. Math. Biol. 67 (2005) 211–259. (doi: 10.1016/j.bulm.2004.08.001)

  4. J.S. Lowengrub, Z. Hu, S.M. Wise, J.S. Kim, and A. Voigt, Phase-Field Modeling of Step Dynamics, MRS Proceedings, 859E (2005) JJ8.6.1–JJ8.6.6.

  5. S.M. Wise, J.S. Lowengrub, J.S. Kim, and W.C. Johnson, Efficient Phase-Field Simulation of Quantum Dot Formation in a Strained Heteroepitaxial Film, Superlattices and Microstructures 36 (2004) 293–304. (doi: 10.1016/j.spmi.2004.08.029)

  6. S.M. Wise, J.S. Kim, and W.C. Johnson, Surface-Directed Spinodal Decomposition in a Stressed Two-Dimensional Thin Film, Thin Solid Films 473 (2004) 151–163. (doi: 10.1016/j.tsf.2004.07.075)

  7. S.M. Wise and W.C. Johnson, Numerical Simulations of Pattern-Directed Phase Decomposition in a Stressed, Binary Thin Film, J. Appl. Phys. 94 (2003) 889–898. (doi: 10.1063/1.1577230)

  8. W.C. Johnson, S.M. Wise, J.Y. Huh, and J. Favergeon, Effect of Interfacial Segregation on Phase Decomposition of a Thin Film on a Patterned Substrate, Met. Mater. Int. 9 (2003) 1–8. (doi: 10.1007/BF03027222)

  9. W.C. Johnson and S.M. Wise, Phase Decomposition of a Binary Thin Film on a Patterned Substrate, Appl. Phys. Lettr. 81 (2002), 919–921. (doi: 10.1063/1.1497193)

  10. S.M. Wise and W.C. Johnson, Competitive Phase Growth in Stressed Thin Films, Modeling the Performance of Engineering Structural Materials II (TMS Fall 2001 Meeting), (2001).

  11. W.C. Johnson, P.H. Leo, Y. Zhen, and S.M. Wise, Spinodal Decomposition in Thin Plates Subjected to a Temperature Gradient, Modeling the Performance of Engineering Structural Materials II (TMS Fall 2001 Meeting), (2001).

  12. S.M. Wise, A.J. Sommese, and L.T. Watson, Algorithm 801: POLSYS_PLP: A Partitioned Linear Product Homotopy Code for Solving Polynomial Systems of Equations, ACM TOMS 26 (2000) 176–200. (doi: 10.1145/347837.347885)

  13. D. Schaal and S.M. Wise, Rado Numbers for Some Inequalities and an Arbitrary Number of Colors, Congr. Numer. 121 (1996), 147–153.