Edit Profile (opens in new tab) Lowengrub, John Samuel Co-Author Distance Author ID: lowengrub.john-s Published as: Lowengrub, John; Lowengrub, John S.; Lowengrub, J. S.; Lowengrub, J. more...less Homepage: http://www.math.uci.edu/~lowengrb/ External Links: MGP Documents Indexed: 116 Publications since 1989, including 1 Additional arXiv Preprint Co-Authors: 124 Co-Authors with 115 Joint Publications 3,953 Co-Co-Authors all top 5 Co-Authors 1 single-authored 19 Wise, Steven M. 18 Li, Shuwang 14 Hou, Thomas Yizhao 12 Cristini, Vittorio 12 Voigt, Axel 9 Wang, Cheng 8 Shelley, Michael J. 7 Macklin, Paul 6 Guo, Zhenlin 5 Beale, J. Thomas 5 Guan, Zhen 5 Li, Xiaofan 5 Zhao, Meng 4 Aland, Sebastian 4 Chen, Ying 4 Frieboes, Hermann B. 4 Goodman, Jonathan B. 4 Kim, Junseok 4 Li, Xiangrong 4 Lin, Ping 4 Xu, Jianjun 4 Zheng, Xiaoming 3 Baskaran, Arvind 3 Belmonte, Andrew 3 Chaplain, Mark A. J. 3 Hu, Zhengzheng 3 James, Ashley J. 3 Jin, Fang 3 Konstorum, Anna 3 Lee, Hyeong-Gi 3 Leo, Perry H. 3 Liu, Chun 3 Liu, Kai 3 Nie, Qing 3 Rätz, Andreas 3 Ying, Wenjun 3 Zhao, Hongkai 2 Allard, Jun 2 Barua, Amlan K. 2 Caflisch, Russel E. 2 Chuang, Yao-Li 2 Feng, Wenqiang 2 Kang, Kyungkeun 2 Li, Zhilin 2 Lu, Min-Jhe 2 McDougall, Steven R. 2 Pham, Kara 2 Sohn, Jinsun 2 Teigen, Knut Erik 2 Truskinovsky, Lev 2 Turian, Emma 2 Zhao, Kun 1 Anderson, Alexander R. A. 1 Anderson, Anthony M. 1 Angenent, Sigurd Bernardus 1 Anjos, Pedro 1 Aronson, Donald G. 1 Balcerak, Michal 1 Bellomo, Nicola 1 Betelú, Santiago I. 1 Bingham, Richard 1 Byrne, Helen Mary 1 Chauvière, Arnaud 1 Cheng, Qing 1 Chew, Ray 1 Cox, Geoffrey 1 Dosi, Giovanni 1 Egerer, Sabine 1 Ezhov, Ivan 1 Feng, Hualong 1 Forni, Guido 1 Franco-de-Leon, Mariano 1 Hao, Wenrui 1 Hatzikirou, Haralambos 1 Hausser, Frank 1 He, Ong 1 Heinonen, Vili 1 Hillen, Thomas 1 Jackson, Trachette L. 1 Jou, Herng-Jeng 1 Karnakov, Petr 1 Knopoff, Damian A. 1 Komarova, Natalia L. 1 Koumoutsakos, Petros D. 1 Krasny, Robert 1 Lander, Arthur D. 1 Lervåg, Karl Yngve 1 Leung, Shingyu 1 Li, Bo 1 Li, Jonathan F. 1 Litvinov, Sergey 1 Longmire, Ellen K. 1 Lopes Filho, Milton da Costa 1 Marth, Wieland 1 Menze, Bjoern H. 1 Merriman, Barry 1 Münch, Andreas 1 Niroobakhsh, Zahra 1 Nussenzveig Lopes, Helena Judith 1 Shelly, M. J. ...and 24 more Co-Authors all top 5 Serials 31 Journal of Computational Physics 11 Journal of Theoretical Biology 6 Journal of Mathematical Biology 5 SIAM Journal on Numerical Analysis 5 Communications in Mathematical Sciences 5 Communications in Computational Physics 4 Physics of Fluids 3 Communications on Pure and Applied Mathematics 3 Bulletin of Mathematical Biology 3 SIAM Journal on Scientific Computing 2 Computer Methods in Applied Mechanics and Engineering 2 Journal of Fluid Mechanics 2 Nonlinearity 2 Journal of Computational and Applied Mathematics 2 Physica D 2 Mathematical and Computer Modelling 2 Journal of Scientific Computing 2 Advances in Computational Mathematics 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Mathematical Methods in the Applied Sciences 1 Mathematics of Computation 1 European Journal of Applied Mathematics 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 SIAM Journal on Applied Mathematics 1 Interfaces and Free Boundaries 1 CMES. Computer Modeling in Engineering & Sciences 1 Discrete and Continuous Dynamical Systems. Series B 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 FDMP. Fluid Dynamics & Materials Processing 1 Journal of Biological Dynamics 1 Statistical Analysis and Data Mining 1 International Journal for Numerical Methods in Biomedical Engineering 1 International Journal of Biomathematics and Biostatistics all top 5 Fields 62 Fluid mechanics (76-XX) 50 Numerical analysis (65-XX) 40 Biology and other natural sciences (92-XX) 39 Partial differential equations (35-XX) 14 Mechanics of deformable solids (74-XX) 10 Statistical mechanics, structure of matter (82-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Integral equations (45-XX) 2 Systems theory; control (93-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Quantum theory (81-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 103 Publications have been cited 4,572 times in 2,391 Documents Cited by ▼ Year ▼ Quasi-incompressible Cahn-Hilliard fluids and topological transitions. Zbl 0927.76007 Lowengrub, J.; Truskinovsky, L. 365 1998 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. 271 2009 Removing the stiffness from interfacial flows with surface tension. Zbl 0810.76095 Hou, Thomas Y.; Lowengrub, John S.; Shelley, Michael J. 224 1994 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. 203 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 200 2008 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. 166 2010 Conservative multigrid methods for Cahn–Hilliard fluids. Zbl 1109.76348 Kim, Junseok; Kang, Kyungkeun; Lowengrub, John 151 2004 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. 128 2013 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. 118 2009 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. 114 2014 Nonlinear simulation of tumor growth. Zbl 1023.92013 Cristini, Vittorio; Lowengrub, John; Nie, Qing 100 2003 Solving the regularized, strongly anisotropic Cahn-Hilliard equation by an adaptive nonlinear multigrid method. Zbl 1310.82044 Wise, Steven; Kim, Junseok; Lowengrub, John 94 2007 A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactant. Zbl 1061.76062 James, Ashley J.; Lowengrub, John 90 2004 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 88 2013 A level-set method for interfacial flows with surfactant. Zbl 1161.76548 Xu, Jian-Jun; Li, Zhilin; Lowengrub, John; Zhao, Hongkai 88 2006 A diffuse-interface method for two-phase flows with soluble surfactants. Zbl 1428.76210 Teigen, Knut Erik; Song, Peng; Lowengrub, John; Voigt, Axel 84 2011 Solving PDEs in complex geometries: a diffuse domain approach. Zbl 1178.35027 Li, X.; Lowengrub, J.; Rätz, A.; Voigt, A. 76 2009 Multiscale modelling and nonlinear simulation of vascular tumour growth. Zbl 1311.92040 Macklin, Paul; McDougall, Steven; Anderson, Alexander R. A.; Chaplain, Mark A. J.; Cristini, Vittorio; Lowengrub, John 76 2009 Phase field modeling and simulation of three-phase flows. Zbl 1100.35088 Kim, Junseok; Lowengrub, John 73 2005 Modeling pinchoff and reconnection in a Hele-Shaw cell. I: The models and their calibration. Zbl 1184.76316 Lee, Hyeong-Gi; Lowengrub, J. S.; Goodman, J. 72 2002 A new phase-field model for strongly anisotropic systems. Zbl 1186.80014 Torabi, Solmaz; Lowengrub, John; Voigt, Axel; Wise, Steven 71 2009 Boundary integral methods for multicomponent fluids and multiphase materials. Zbl 1046.76029 Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J. 70 2001 The long-time motion of vortex sheets with surface tension. Zbl 1185.76545 Hou, T. Y.; Lowengrub, J. S.; Shelly, M. J. 69 1997 Growth rates for the linearized motion of fluid interfaces away from equilibrium. Zbl 0796.76041 Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John S. 68 1993 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 66 2010 Modeling pinchoff and reconnection in a Hele-Shaw cell. II: Analysis and simulation in the nonlinear regime. Zbl 1184.76317 Lee, Hyeong-Gi; Lowengrub, J. S.; Goodman, J. 57 2002 An adaptive coupled level-set/volume-of-fluid interface capturing method for unstructured triangular grids. Zbl 1160.76377 Yang, Xiaofeng; James, Ashley J.; Lowengrub, John; Zheng, Xiaoming; Cristini, Vittorio 55 2006 A numerical method for the quasi-incompressible Cahn-Hilliard-Navier-Stokes equations for variable density flows with a discrete energy law. Zbl 1349.76057 Guo, Z.; Lin, P.; Lowengrub, J. S. 54 2014 A multiscale model of virus pandemic: heterogeneous interactive entities in a globally connected world. Zbl 1451.92276 Bellomo, Nicola; Bingham, Richard; Chaplain, Mark A. J.; Dosi, Giovanni; Forni, Guido; Knopoff, Damian A.; Lowengrub, John; Twarock, Reidun; Virgillito, Maria Enrica 54 2020 A diffuse-interface approach for modelling transport, diffusion and adsorption/desorption of material quantities on a deformable interface. Zbl 1186.35168 Teigen, Knut Erik; Li, Xiangrong; Lowengrub, John; Wang, Fan; Voigt, Axel 51 2009 Microstructural evolution in inhomogeneous elastic media. Zbl 0880.73050 Jou, H.-J.; Leo, P. H.; Lowengrub, J. S. 50 1997 An adaptive multigrid algorithm for simulating solid tumor growth using mixture models. Zbl 1211.65123 Wise, S. M.; Lowengrub, J. S.; Cristini, V. 50 2011 Convergence of the point vortex method for the 2-D Euler equations. Zbl 0694.76013 Goodman, Jonathan; Hou, Thomas Y.; Lowengrub, John 49 1990 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. 49 2017 Convergence analysis for second-order accurate schemes for the periodic nonlocal Allen-Cahn and Cahn-Hilliard equations. Zbl 1387.65087 Guan, Zhen; Lowengrub, John; Wang, Cheng 46 2017 Conservative multigrid methods for ternary Cahn-Hilliard systems. Zbl 1085.65093 Kim, Junseok; Kang, Kyungkeun; Lowengrub, John 43 2004 Evolving interfaces via gradients of geometry-dependent interior Poisson problems: application to tumor growth. Zbl 1067.65111 Macklin, Paul; Lowengrub, John 43 2005 Analysis of a mixture model of tumor growth. Zbl 1292.35153 Lowengrub, John; Titi, Edriss; Zhao, Kun 42 2013 A grid based particle method for solving partial differential equations on evolving surfaces and modeling high order geometrical motion. Zbl 1316.65089 Leung, Shingyu; Lowengrub, John; Zhao, Hongkai 39 2011 Diffuse interface models of locally inextensible vesicles in a viscous fluid. Zbl 1349.76933 Aland, Sebastian; Egerer, Sabine; Lowengrub, John; Voigt, Axel 37 2014 Adaptive unstructured volume remeshing. II: Application to two- and three-dimensional level-set simulations of multiphase flow. Zbl 1075.65120 Zheng, Xiaoming; Lowengrub, John; Anderson, Anthony; Cristini, Vittorio 37 2005 An improved geometry-aware curvature discretization for level set methods: Application to tumor growth. Zbl 1089.92024 Macklin, Paul; Lowengrub, John 34 2006 Nonlinear simulation of the effect of microenvironment on tumor growth. Zbl 1451.92102 Macklin, Paul; Lowengrub, John 33 2007 Convergence of a boundary integral method for water waves. Zbl 0858.76046 Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John 32 1996 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 30 2018 Two-phase flow in complex geometries: a diffuse domain approach. Zbl 1231.76200 Aland, S.; Lowengrub, J.; Voigt, A. 30 2010 A new ghost cell/level set method for moving boundary problems: application to tumor growth. Zbl 1203.65144 Macklin, Paul; Lowengrub, John S. 27 2008 Dynamics of multicomponent vesicles in a viscous fluid. Zbl 1381.76053 Sohn, Jin Sun; Tseng, Yu-Hau; Li, Shuwang; Voigt, Axel; Lowengrub, John S. 26 2010 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 24 2018 Numerical evidence of nonuniqueness in the evolution of vortex sheets. Zbl 1124.76010 Lopes Filho, Milton C.; Lowengrub, John; Nussenzveig Lopes, Helena J.; Zheng, Yuxi 23 2006 Microstructural evolution in orthotropic elastic media. Zbl 0960.74076 Leo, P. H.; Lowengrub, J. S.; Nie, Qing 22 2000 Nonlinear three-dimensional simulation of solid tumor growth. Zbl 1124.92022 Li, Xiangrong; Cristini, Vittorio; Nie, Qing; Lowengrub, John S. 21 2007 A rescaling scheme with application to the long-time simulation of viscous fingering in a Hele-Shaw cell. Zbl 1343.76048 Li, Shuwang; Lowengrub, John S.; Leo, Perry H. 20 2007 Geometric evolution laws for thin crystalline films: modeling and numerics. Zbl 1364.74062 Li, Bo; Lowengrub, John; Ratz, Andreas; Voigt, Axel 17 2009 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. 17 2018 Convergence of the vortex method for vortex sheets. Zbl 0676.76023 Caflisch, Russel E.; Lowengrub, John S. 17 1989 Density-dependent quiescence in glioma invasion: instability in a simple reaction-diffusion model for the migration/proliferation dichotomy. Zbl 1448.92064 Pham, Kara; Chauviere, Arnaud; Hatzikirou, Haralambos; Li, Xiangrong; Byrne, Helen M.; Cristini, Vittorio; Lowengrub, John 17 2012 Multispecies model of cell lineages and feedback control in solid tumors. Zbl 1397.92381 Youssefpour, H.; Li, X.; Lander, A. D.; Lowengrub, J. S. 16 2012 Analysis of the diffuse-domain method for solving PDEs in complex geometries. Zbl 1328.65223 Lervåg, Karl Yngve; Lowengrub, John 13 2015 Focusing of an elongated hole in porous medium flow. Zbl 0989.35082 Angenent, S. B.; Aronson, D. G.; Betelu, S. I.; Lowengrub, J. S. 13 2001 The effect of interstitial pressure on tumor growth: coupling with the blood and lymphatic vascular systems. Zbl 1406.92330 Wu, Min; Frieboes, Hermann B.; McDougall, Steven R.; Chaplain, Mark A. J.; Cristini, Vittorio; Lowengrub, John 13 2013 A diffuse domain method for two-phase flows with large density ratio in complex geometries. Zbl 1461.76447 Guo, Zhenlin; Yu, Fei; Lin, Ping; Wise, Steven; Lowengrub, John 13 2021 Convergence of the point vortex method for the 3-D Euler equations. Zbl 0856.76059 Hou, Thomas Y.; Lowengrub, John 12 1990 A continuum model of colloid-stabilized interfaces. Zbl 1308.76159 Aland, Sebastian; Lowengrub, John; Voigt, Axel 12 2011 High-order and efficient methods for the vorticity formulation of the Euler equations. Zbl 0815.76068 Lowengrub, J. S.; Shelley, M. J.; Merriman, B. 11 1993 Convergence of a point vortex method for vortex sheets. Zbl 0799.76062 Hou, Thomas Y.; Lowengrub, John; Krasny, Robert 10 1991 Thermodynamically consistent models for two-component vesicles. Zbl 1306.92014 Haußer, Frank; Marth, Wieland; Li, Shuwang; Lowengrub, John; Rätz, Andreas; Voigt, Axel 9 2013 Computation of a shrinking interface in a Hele-Shaw cell. Zbl 1396.76029 Zhao, Meng; Li, Xiaofan; Ying, Wenjun; Belmonte, Andrew; Lowengrub, John; Li, Shuwang 9 2018 Tumor growth in complex, evolving microenvironmental geometries: a diffuse domain approach. Zbl 1303.92042 Chen, Ying; Lowengrub, John S. 9 2014 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. 9 2016 Numerical simulation of endocytosis: viscous flow driven by membranes with non-uniformly distributed curvature-inducing molecules. Zbl 1351.76067 Lowengrub, John; Allard, Jun; Aland, Sebastian 9 2016 Feedback regulation in a cancer stem cell model can cause an Allee effect. Zbl 1341.92029 Konstorum, Anna; Hillen, Thomas; Lowengrub, John 9 2016 Surface phase separation and flow in a simple model of multicomponent drops and vesicles. Zbl 1153.76441 Lowengrub, J. S.; Xu, J-J.; Voigt, A. 9 2007 Topological transitions in liquid/liquid interfaces. Zbl 0929.35191 Lowengrub, J. S.; Goodman, J.; Lee, H.; Longmire, E. K.; Shelley, M. J.; Truskinovsky, L. 8 1999 An interface-fitted adaptive mesh method for elliptic problems and its application in free interface problems with surface tension. Zbl 1357.65271 Zheng, Xiaoming; Lowengrub, John 8 2016 Numerical study of surfactant-laden drop-drop interactions. Zbl 1364.76165 Xu, Jian-Jun; Li, Zhilin; Lowengrub, John; Zhao, Hongkai 8 2011 Nonlinear studies of tumor morphological stability using a two-fluid flow model. Zbl 1407.76031 Pham, Kara; Turian, Emma; Liu, Kai; Li, Shuwang; Lowengrub, John 7 2018 Spatial and temporal stability issues for interfacial flows with surface tension. Zbl 0816.76050 Beale, J. T.; Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J. 7 1994 Locomotion, wrinkling, and budding of a multicomponent vesicle in viscous fluids. Zbl 1282.35420 Li, Shuwang; Lowengrub, John; Voigt, Axel 7 2012 The effects of cell compressibility, motility and contact inhibition on the growth of tumor cell clusters using the cellular Potts model. Zbl 1411.92140 Li, Jonathan F.; Lowengrub, John 6 2014 Modeling an elastic fingering instability in a reactive Hele-Shaw flow. Zbl 1343.76011 He, Ong; Lowengrub, John; Belmonte, Andrew 6 2012 Higher-order accurate diffuse-domain methods for partial differential equations with Dirichlet boundary conditions in complex, evolving geometries. Zbl 1453.65306 Yu, Fei; Guo, Zhenlin; Lowengrub, John 6 2020 Nonlinear simulations of elastic fingering in a Hele-Shaw cell. Zbl 1382.76071 Zhao, Meng; Belmonte, Andrew; Li, Shuwang; Li, Xiaofan; Lowengrub, John 6 2016 An efficient rescaling algorithm for simulating the evolution of multiple elastically stressed precipitates. Zbl 1373.74079 Barua, Amlan K.; Li, Shuwang; Feng, Hualong; Li, Xiaofan; Lowengrub, John 5 2013 The effect of spontaneous curvature on a two-phase vesicle. Zbl 1325.92028 Cox, Geoffrey; Lowengrub, John 5 2015 The convergence of an exact desingularization for vortex methods. Zbl 0769.76045 Hou, T. Y.; Lowengrub, J.; Shelley, M. J. 4 1993 Axisymmetric multicomponent vesicles: a comparison of hydrodynamic and geometric models. Zbl 1310.92018 Sohn, Jinsun; Li, Shuwang; Li, Xiaofan; Lowengrub, John S. 4 2012 An efficient adaptive rescaling scheme for computing moving interface problems. Zbl 1490.76088 Zhao, Meng; Ying, Wenjun; Lowengrub, John; Li, Shuwang 4 2017 Complex far-field geometries determine the stability of solid tumor growth with chemotaxis. Zbl 1439.92044 Lu, Min-Jhe; Liu, Chun; Lowengrub, John; Li, Shuwang 4 2020 Three-dimensional spatiotemporal modeling of colon cancer organoids reveals that multimodal control of stem cell self-renewal is a critical determinant of size and shape in early stages of tumor growth. Zbl 1394.92068 Yan, Huaming; Konstorum, Anna; Lowengrub, John S. 3 2018 Almost optimal convergence of the point vortex method for vortex sheets using numerical filtering. Zbl 0935.76068 Caflisch, Russel E.; Hou, Thomas Y.; Lowengrub, John 3 1999 Tumor growth and calcification in evolving microenvironmental geometries. Zbl 1406.92287 Chen, Ying; Lowengrub, John S. 3 2019 A level-set continuum method for two-phase flows with insoluble surfactant. Zbl 1522.76105 Xu, Jian-Jun; Yang, Yin; Lowengrub, John 3 2012 Nonlinear limiting dynamics of a shrinking interface in a Hele-Shaw cell. Zbl 1461.76143 Zhao, Meng; Niroobakhsh, Zahra; Lowengrub, John; Li, Shuwang 3 2021 Energy stable multigrid method for local and non-local hydrodynamic models for freezing. Zbl 1423.80022 Baskaran, Arvind; Guan, Zhen; Lowengrub, John 2 2016 Morphological stability of an elastic tumor-host interface. Zbl 1451.74171 Turian, Emma; Liu, Kai; Lowengrub, John; Li, Shuwang 2 2019 Stability of boundary integral methods for water waves. Zbl 0885.35095 Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John 2 1997 Exact desingularization and local regridding for vortex methods. Zbl 0825.76647 Hou, T. Y.; Lowengrub, J.; Shelley, M. J. 2 1991 Nonlinear simulation of vascular tumor growth with chemotaxis and the control of necrosis. Zbl 07525143 Lu, Min-Jhe; Hao, Wenrui; Liu, Chun; Lowengrub, John; Li, Shuwang 2 2022 Second order approximation for a quasi-incompressible Navier-Stokes Cahn-Hilliard system of two-phase flows with variable density. Zbl 07516811 Guo, Zhenlin; Cheng, Qing; Lin, Ping; Liu, Chun; Lowengrub, John 2 2022 Nonlinear simulation of vascular tumor growth with chemotaxis and the control of necrosis. Zbl 07525143 Lu, Min-Jhe; Hao, Wenrui; Liu, Chun; Lowengrub, John; Li, Shuwang 2 2022 Second order approximation for a quasi-incompressible Navier-Stokes Cahn-Hilliard system of two-phase flows with variable density. Zbl 07516811 Guo, Zhenlin; Cheng, Qing; Lin, Ping; Liu, Chun; Lowengrub, John 2 2022 Tumor growth towards lower extracellular matrix conductivity regions under Darcy’s law and steady morphology. Zbl 1496.92014 Zheng, Xiaoming; Zhao, Kun; Jackson, Trachette; Lowengrub, John 1 2022 A diffuse domain method for two-phase flows with large density ratio in complex geometries. Zbl 1461.76447 Guo, Zhenlin; Yu, Fei; Lin, Ping; Wise, Steven; Lowengrub, John 13 2021 Nonlinear limiting dynamics of a shrinking interface in a Hele-Shaw cell. Zbl 1461.76143 Zhao, Meng; Niroobakhsh, Zahra; Lowengrub, John; Li, Shuwang 3 2021 A multiscale model of virus pandemic: heterogeneous interactive entities in a globally connected world. Zbl 1451.92276 Bellomo, Nicola; Bingham, Richard; Chaplain, Mark A. J.; Dosi, Giovanni; Forni, Guido; Knopoff, Damian A.; Lowengrub, John; Twarock, Reidun; Virgillito, Maria Enrica 54 2020 Higher-order accurate diffuse-domain methods for partial differential equations with Dirichlet boundary conditions in complex, evolving geometries. Zbl 1453.65306 Yu, Fei; Guo, Zhenlin; Lowengrub, John 6 2020 Complex far-field geometries determine the stability of solid tumor growth with chemotaxis. Zbl 1439.92044 Lu, Min-Jhe; Liu, Chun; Lowengrub, John; Li, Shuwang 4 2020 Tumor growth and calcification in evolving microenvironmental geometries. Zbl 1406.92287 Chen, Ying; Lowengrub, John S. 3 2019 Morphological stability of an elastic tumor-host interface. Zbl 1451.74171 Turian, Emma; Liu, Kai; Lowengrub, John; Li, Shuwang 2 2019 Boundary integral methods for dispersive equations, Airy flow and the modified Korteweg de Vries equation. Zbl 1422.65241 Franco-de-Leon, Mariano; Lowengrub, John 1 2019 Efficient simulation of thermally fluctuating biopolymers immersed in fluids on 1-micron, 1-second scales. Zbl 1452.74038 Liu, Kai; Lowengrub, John; Allard, Jun 1 2019 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 30 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 24 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. 17 2018 Computation of a shrinking interface in a Hele-Shaw cell. Zbl 1396.76029 Zhao, Meng; Li, Xiaofan; Ying, Wenjun; Belmonte, Andrew; Lowengrub, John; Li, Shuwang 9 2018 Nonlinear studies of tumor morphological stability using a two-fluid flow model. Zbl 1407.76031 Pham, Kara; Turian, Emma; Liu, Kai; Li, Shuwang; Lowengrub, John 7 2018 Three-dimensional spatiotemporal modeling of colon cancer organoids reveals that multimodal control of stem cell self-renewal is a critical determinant of size and shape in early stages of tumor growth. Zbl 1394.92068 Yan, Huaming; Konstorum, Anna; Lowengrub, John S. 3 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. 49 2017 Convergence analysis for second-order accurate schemes for the periodic nonlocal Allen-Cahn and Cahn-Hilliard equations. Zbl 1387.65087 Guan, Zhen; Lowengrub, John; Wang, Cheng 46 2017 An efficient adaptive rescaling scheme for computing moving interface problems. Zbl 1490.76088 Zhao, Meng; Ying, Wenjun; Lowengrub, John; Li, Shuwang 4 2017 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. 9 2016 Numerical simulation of endocytosis: viscous flow driven by membranes with non-uniformly distributed curvature-inducing molecules. Zbl 1351.76067 Lowengrub, John; Allard, Jun; Aland, Sebastian 9 2016 Feedback regulation in a cancer stem cell model can cause an Allee effect. Zbl 1341.92029 Konstorum, Anna; Hillen, Thomas; Lowengrub, John 9 2016 An interface-fitted adaptive mesh method for elliptic problems and its application in free interface problems with surface tension. Zbl 1357.65271 Zheng, Xiaoming; Lowengrub, John 8 2016 Nonlinear simulations of elastic fingering in a Hele-Shaw cell. Zbl 1382.76071 Zhao, Meng; Belmonte, Andrew; Li, Shuwang; Li, Xiaofan; Lowengrub, John 6 2016 Energy stable multigrid method for local and non-local hydrodynamic models for freezing. Zbl 1423.80022 Baskaran, Arvind; Guan, Zhen; Lowengrub, John 2 2016 Analysis of the diffuse-domain method for solving PDEs in complex geometries. Zbl 1328.65223 Lervåg, Karl Yngve; Lowengrub, John 13 2015 The effect of spontaneous curvature on a two-phase vesicle. Zbl 1325.92028 Cox, Geoffrey; Lowengrub, John 5 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. 114 2014 A numerical method for the quasi-incompressible Cahn-Hilliard-Navier-Stokes equations for variable density flows with a discrete energy law. Zbl 1349.76057 Guo, Z.; Lin, P.; Lowengrub, J. S. 54 2014 Diffuse interface models of locally inextensible vesicles in a viscous fluid. Zbl 1349.76933 Aland, Sebastian; Egerer, Sabine; Lowengrub, John; Voigt, Axel 37 2014 Tumor growth in complex, evolving microenvironmental geometries: a diffuse domain approach. Zbl 1303.92042 Chen, Ying; Lowengrub, John S. 9 2014 The effects of cell compressibility, motility and contact inhibition on the growth of tumor cell clusters using the cellular Potts model. Zbl 1411.92140 Li, Jonathan F.; Lowengrub, John 6 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. 128 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 88 2013 Analysis of a mixture model of tumor growth. Zbl 1292.35153 Lowengrub, John; Titi, Edriss; Zhao, Kun 42 2013 The effect of interstitial pressure on tumor growth: coupling with the blood and lymphatic vascular systems. Zbl 1406.92330 Wu, Min; Frieboes, Hermann B.; McDougall, Steven R.; Chaplain, Mark A. J.; Cristini, Vittorio; Lowengrub, John 13 2013 Thermodynamically consistent models for two-component vesicles. Zbl 1306.92014 Haußer, Frank; Marth, Wieland; Li, Shuwang; Lowengrub, John; Rätz, Andreas; Voigt, Axel 9 2013 An efficient rescaling algorithm for simulating the evolution of multiple elastically stressed precipitates. Zbl 1373.74079 Barua, Amlan K.; Li, Shuwang; Feng, Hualong; Li, Xiaofan; Lowengrub, John 5 2013 Density-dependent quiescence in glioma invasion: instability in a simple reaction-diffusion model for the migration/proliferation dichotomy. Zbl 1448.92064 Pham, Kara; Chauviere, Arnaud; Hatzikirou, Haralambos; Li, Xiangrong; Byrne, Helen M.; Cristini, Vittorio; Lowengrub, John 17 2012 Multispecies model of cell lineages and feedback control in solid tumors. Zbl 1397.92381 Youssefpour, H.; Li, X.; Lander, A. D.; Lowengrub, J. S. 16 2012 Locomotion, wrinkling, and budding of a multicomponent vesicle in viscous fluids. Zbl 1282.35420 Li, Shuwang; Lowengrub, John; Voigt, Axel 7 2012 Modeling an elastic fingering instability in a reactive Hele-Shaw flow. Zbl 1343.76011 He, Ong; Lowengrub, John; Belmonte, Andrew 6 2012 Axisymmetric multicomponent vesicles: a comparison of hydrodynamic and geometric models. Zbl 1310.92018 Sohn, Jinsun; Li, Shuwang; Li, Xiaofan; Lowengrub, John S. 4 2012 A level-set continuum method for two-phase flows with insoluble surfactant. Zbl 1522.76105 Xu, Jian-Jun; Yang, Yin; Lowengrub, John 3 2012 A diffuse-interface method for two-phase flows with soluble surfactants. Zbl 1428.76210 Teigen, Knut Erik; Song, Peng; Lowengrub, John; Voigt, Axel 84 2011 An adaptive multigrid algorithm for simulating solid tumor growth using mixture models. Zbl 1211.65123 Wise, S. M.; Lowengrub, J. S.; Cristini, V. 50 2011 A grid based particle method for solving partial differential equations on evolving surfaces and modeling high order geometrical motion. Zbl 1316.65089 Leung, Shingyu; Lowengrub, John; Zhao, Hongkai 39 2011 A continuum model of colloid-stabilized interfaces. Zbl 1308.76159 Aland, Sebastian; Lowengrub, John; Voigt, Axel 12 2011 Numerical study of surfactant-laden drop-drop interactions. Zbl 1364.76165 Xu, Jian-Jun; Li, Zhilin; Lowengrub, John; Zhao, Hongkai 8 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. 166 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 66 2010 Two-phase flow in complex geometries: a diffuse domain approach. Zbl 1231.76200 Aland, S.; Lowengrub, J.; Voigt, A. 30 2010 Dynamics of multicomponent vesicles in a viscous fluid. Zbl 1381.76053 Sohn, Jin Sun; Tseng, Yu-Hau; Li, Shuwang; Voigt, Axel; Lowengrub, John S. 26 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. 271 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. 203 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. 118 2009 Solving PDEs in complex geometries: a diffuse domain approach. Zbl 1178.35027 Li, X.; Lowengrub, J.; Rätz, A.; Voigt, A. 76 2009 Multiscale modelling and nonlinear simulation of vascular tumour growth. Zbl 1311.92040 Macklin, Paul; McDougall, Steven; Anderson, Alexander R. A.; Chaplain, Mark A. J.; Cristini, Vittorio; Lowengrub, John 76 2009 A new phase-field model for strongly anisotropic systems. Zbl 1186.80014 Torabi, Solmaz; Lowengrub, John; Voigt, Axel; Wise, Steven 71 2009 A diffuse-interface approach for modelling transport, diffusion and adsorption/desorption of material quantities on a deformable interface. Zbl 1186.35168 Teigen, Knut Erik; Li, Xiangrong; Lowengrub, John; Wang, Fan; Voigt, Axel 51 2009 Geometric evolution laws for thin crystalline films: modeling and numerics. Zbl 1364.74062 Li, Bo; Lowengrub, John; Ratz, Andreas; Voigt, Axel 17 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 200 2008 A new ghost cell/level set method for moving boundary problems: application to tumor growth. Zbl 1203.65144 Macklin, Paul; Lowengrub, John S. 27 2008 Solving the regularized, strongly anisotropic Cahn-Hilliard equation by an adaptive nonlinear multigrid method. Zbl 1310.82044 Wise, Steven; Kim, Junseok; Lowengrub, John 94 2007 Nonlinear simulation of the effect of microenvironment on tumor growth. Zbl 1451.92102 Macklin, Paul; Lowengrub, John 33 2007 Nonlinear three-dimensional simulation of solid tumor growth. Zbl 1124.92022 Li, Xiangrong; Cristini, Vittorio; Nie, Qing; Lowengrub, John S. 21 2007 A rescaling scheme with application to the long-time simulation of viscous fingering in a Hele-Shaw cell. Zbl 1343.76048 Li, Shuwang; Lowengrub, John S.; Leo, Perry H. 20 2007 Surface phase separation and flow in a simple model of multicomponent drops and vesicles. Zbl 1153.76441 Lowengrub, J. S.; Xu, J-J.; Voigt, A. 9 2007 A level-set method for interfacial flows with surfactant. Zbl 1161.76548 Xu, Jian-Jun; Li, Zhilin; Lowengrub, John; Zhao, Hongkai 88 2006 An adaptive coupled level-set/volume-of-fluid interface capturing method for unstructured triangular grids. Zbl 1160.76377 Yang, Xiaofeng; James, Ashley J.; Lowengrub, John; Zheng, Xiaoming; Cristini, Vittorio 55 2006 An improved geometry-aware curvature discretization for level set methods: Application to tumor growth. Zbl 1089.92024 Macklin, Paul; Lowengrub, John 34 2006 Numerical evidence of nonuniqueness in the evolution of vortex sheets. Zbl 1124.76010 Lopes Filho, Milton C.; Lowengrub, John; Nussenzveig Lopes, Helena J.; Zheng, Yuxi 23 2006 Phase field modeling and simulation of three-phase flows. Zbl 1100.35088 Kim, Junseok; Lowengrub, John 73 2005 Evolving interfaces via gradients of geometry-dependent interior Poisson problems: application to tumor growth. Zbl 1067.65111 Macklin, Paul; Lowengrub, John 43 2005 Adaptive unstructured volume remeshing. II: Application to two- and three-dimensional level-set simulations of multiphase flow. Zbl 1075.65120 Zheng, Xiaoming; Lowengrub, John; Anderson, Anthony; Cristini, Vittorio 37 2005 Conservative multigrid methods for Cahn–Hilliard fluids. Zbl 1109.76348 Kim, Junseok; Kang, Kyungkeun; Lowengrub, John 151 2004 A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactant. Zbl 1061.76062 James, Ashley J.; Lowengrub, John 90 2004 Conservative multigrid methods for ternary Cahn-Hilliard systems. Zbl 1085.65093 Kim, Junseok; Kang, Kyungkeun; Lowengrub, John 43 2004 Nonlinear simulation of tumor growth. Zbl 1023.92013 Cristini, Vittorio; Lowengrub, John; Nie, Qing 100 2003 Modeling pinchoff and reconnection in a Hele-Shaw cell. I: The models and their calibration. Zbl 1184.76316 Lee, Hyeong-Gi; Lowengrub, J. S.; Goodman, J. 72 2002 Modeling pinchoff and reconnection in a Hele-Shaw cell. II: Analysis and simulation in the nonlinear regime. Zbl 1184.76317 Lee, Hyeong-Gi; Lowengrub, J. S.; Goodman, J. 57 2002 Boundary integral methods for multicomponent fluids and multiphase materials. Zbl 1046.76029 Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J. 70 2001 Focusing of an elongated hole in porous medium flow. Zbl 0989.35082 Angenent, S. B.; Aronson, D. G.; Betelu, S. I.; Lowengrub, J. S. 13 2001 Microstructural evolution in orthotropic elastic media. Zbl 0960.74076 Leo, P. H.; Lowengrub, J. S.; Nie, Qing 22 2000 Topological transitions in liquid/liquid interfaces. Zbl 0929.35191 Lowengrub, J. S.; Goodman, J.; Lee, H.; Longmire, E. K.; Shelley, M. J.; Truskinovsky, L. 8 1999 Almost optimal convergence of the point vortex method for vortex sheets using numerical filtering. Zbl 0935.76068 Caflisch, Russel E.; Hou, Thomas Y.; Lowengrub, John 3 1999 Quasi-incompressible Cahn-Hilliard fluids and topological transitions. Zbl 0927.76007 Lowengrub, J.; Truskinovsky, L. 365 1998 The long-time motion of vortex sheets with surface tension. Zbl 1185.76545 Hou, T. Y.; Lowengrub, J. S.; Shelly, M. J. 69 1997 Microstructural evolution in inhomogeneous elastic media. Zbl 0880.73050 Jou, H.-J.; Leo, P. H.; Lowengrub, J. S. 50 1997 Stability of boundary integral methods for water waves. Zbl 0885.35095 Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John 2 1997 Convergence of a boundary integral method for water waves. Zbl 0858.76046 Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John 32 1996 Removing the stiffness from interfacial flows with surface tension. Zbl 0810.76095 Hou, Thomas Y.; Lowengrub, John S.; Shelley, Michael J. 224 1994 Spatial and temporal stability issues for interfacial flows with surface tension. Zbl 0816.76050 Beale, J. T.; Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J. 7 1994 Growth rates for the linearized motion of fluid interfaces away from equilibrium. Zbl 0796.76041 Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John S. 68 1993 High-order and efficient methods for the vorticity formulation of the Euler equations. Zbl 0815.76068 Lowengrub, J. S.; Shelley, M. J.; Merriman, B. 11 1993 The convergence of an exact desingularization for vortex methods. Zbl 0769.76045 Hou, T. Y.; Lowengrub, J.; Shelley, M. J. 4 1993 Convergence of a point vortex method for vortex sheets. Zbl 0799.76062 Hou, Thomas Y.; Lowengrub, John; Krasny, Robert 10 1991 Exact desingularization and local regridding for vortex methods. Zbl 0825.76647 Hou, T. Y.; Lowengrub, J.; Shelley, M. J. 2 1991 ...and 3 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,211 Authors 77 Kim, Junseok 74 Yang, Xiaofeng 71 Lowengrub, John Samuel 57 Wang, Cheng 53 Wise, Steven M. 42 Yang, Junxiang 38 Garcke, Harald 32 Li, Yibao 31 Wang, Qi 31 Zhao, Jia 25 Liu, Chun 24 Grasselli, Maurizio 24 Lee, Hyun Geun 23 Chen, Wenbin 23 Shen, Jie 21 Li, Shuwang 21 Qiao, Zhonghua 21 Voigt, Axel 19 Kou, Jisheng 19 Miranville, Alain M. 19 Nürnberg, Robert 18 Gómez, Héctor J. 18 Rocca, Elisabetta 17 Ambrose, David M. 17 Gancedo, Francisco 17 Han, Daozhi 17 Lam, Kei Fong 17 Wang, Xiaoming 17 Zhang, Zhengru 16 Chaplain, Mark A. 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