The Convergence of an Exact Desingularization for Vortex Methods. - Thomas Y. Hou 001; John S. Lowengrub; Michael J. Shelley (SIAM J. Sci. Comput., 1993)

High-Order and Efficient Methods for the Vorticity Formulation of the Euler Equations. - John S. Lowengrub; Michael J. Shelley; Barry Merriman (SIAM J. Sci. Comput., 1993)

Almost optimal convergence of the point vortex method for vortex sheets using numerical filtering. - Russel E. Caflisch; Thomas Y. Hou 001; John S. Lowengrub (Math. Comput., 1999)

An improved geometry-aware curvature discretization for level set methods: Application to tumor growth. - Paul Macklin; John S. Lowengrub (J. Comput. Phys., 2006)

A level-set method for interfacial flows with surfactant. - Jian-Jun Xu; Zhilin Li 002; John S. Lowengrub; Hongkai Zhao (J. Comput. Phys., 2006)

An adaptive coupled level-set/volume-of-fluid interface capturing method for unstructured triangular grids. - Xiaofeng Yang 003; Ashley J. James; John S. Lowengrub; Xiaoming Zheng; Vittorio Cristini (J. Comput. Phys., 2006)

A rescaling scheme with application to the long-time simulation of viscous fingering in a Hele-Shaw cell. - Shuwang Li; John S. Lowengrub; Perry H. Leo (J. Comput. Phys., 2007)

Solving the regularized, strongly anisotropic Cahn-Hilliard equation by an adaptive nonlinear multigrid method. - Steven M. Wise; Junseok Kim; John S. Lowengrub (J. Comput. Phys., 2007)

A New Ghost Cell/Level Set Method for Moving Boundary Problems: Application to Tumor Growth. - Paul Macklin; John S. Lowengrub (J. Sci. Comput., 2008)

Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation. - Zhengzheng Hu; Steven M. Wise; Cheng Wang 015; John S. Lowengrub (J. Comput. Phys., 2009)

An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation. - Steven M. Wise; Cheng Wang 015; John S. Lowengrub (SIAM J. Numer. Anal., 2009)

Dynamics of multicomponent vesicles in a viscous fluid. - Jin Sun Sohn; Yu-Hau Tseng; Shuwang Li; Axel Voigt; John S. Lowengrub (J. Comput. Phys., 2010)

A grid based particle method for solving partial differential equations on evolving surfaces and modeling high order geometrical motion. - Shingyu Leung; John S. Lowengrub; Hongkai Zhao (J. Comput. Phys., 2011)

A diffuse-interface method for two-phase flows with soluble surfactants. - Knut Erik Teigen; Peng Song 016; John S. Lowengrub; Axel Voigt (J. Comput. Phys., 2011)

An adaptive multigrid algorithm for simulating solid tumor growth using mixture models. - Steven M. Wise; John S. Lowengrub; Vittorio Cristini (Math. Comput. Model., 2011)

A level-set continuum method for two-phase flows with insoluble surfactant. - Jian-Jun Xu; Yin Yang 003; John S. Lowengrub (J. Comput. Phys., 2012)

Predicting simulation parameters of biological systems using a Gaussian process model. - Xiangxin Zhu; Max Welling; Fang Jin; John S. Lowengrub (Stat. Anal. Data Min., 2012)

Modeling an Elastic Fingering Instability in a Reactive Hele-Shaw Flow. - Andong He; John S. Lowengrub; Andrew Belmonte (SIAM J. Appl. Math., 2012)

Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation. - Arvind Baskaran; Zhengzheng Hu; John S. Lowengrub; Cheng Wang 015; Steven M. Wise; Peng Zhou (J. Comput. Phys., 2013)

Convergence Analysis of a Second Order Convex Splitting Scheme for the Modified Phase Field Crystal Equation. - Arvind Baskaran; John S. Lowengrub; Cheng Wang 015; Steven M. Wise (SIAM J. Numer. Anal., 2013)

Diffuse interface models of locally inextensible vesicles in a viscous fluid. - Sebastian Aland; Sabine Egerer; John S. Lowengrub; Axel Voigt (J. Comput. Phys., 2014)

Second order convex splitting schemes for periodic nonlocal Cahn-Hilliard and Allen-Cahn equations. - Zhen Guan; John S. Lowengrub; Cheng Wang 015; Steven M. Wise (J. Comput. Phys., 2014)

A numerical method for the quasi-incompressible Cahn-Hilliard-Navier-Stokes equations for variable density flows with a discrete energy law. - Zhenlin Guo; Ping Lin; John S. Lowengrub (J. Comput. Phys., 2014)

POPE: post optimization posterior evaluation of likelihood free models. - Edward Meeds; Michael Chiang; Mary Lee; Olivier Cinquin; John S. Lowengrub; Max Welling (BMC Bioinform., 2015)

An interface-fitted adaptive mesh method for elliptic problems and its application in free interface problems with surface tension. - Xiaoming Zheng; John S. Lowengrub (Adv. Comput. Math., 2016)

Nonlinear simulations of elastic fingering in a Hele-Shaw cell. - Meng Zhao; Andrew Belmonte; Shuwang Li; Xiaofan Li 003; John S. Lowengrub (J. Comput. Appl. Math., 2016)

Collective Properties of a Transcription Initiation Model Under Varying Environment. - Yucheng Hu; John S. Lowengrub (J. Comput. Biol., 2016)

An energy stable, hexagonal finite difference scheme for the 2D phase field crystal amplitude equations. - Zhen Guan; Vili Heinonen; John S. Lowengrub; Cheng Wang 015; Steven M. Wise (J. Comput. Phys., 2016)

Numerical simulation of endocytosis: Viscous flow driven by membranes with non-uniformly distributed curvature-inducing molecules. - John S. Lowengrub; Jun Allard; Sebastian Aland (J. Comput. Phys., 2016)

Feedback, Lineages and Self-Organizing Morphogenesis. - Sameeran Kunche; Huaming Yan; Anne L. Calof; John S. Lowengrub; Arthur D. Lander (PLoS Comput. Biol., 2016)

Automated Unsupervised Segmentation of Liver Lesions in CT scans via Cahn-Hilliard Phase Separation. - Jana Lipková; Markus Rempfler; Patrick Ferdinand Christ; John S. Lowengrub; Bjoern H. Menze (CoRR, 2017)

Multiscale Modeling of Glioblastoma Suggests that the Partial Disruption of Vessel/Cancer Stem Cell Crosstalk Can Promote Tumor Regression Without Increasing Invasiveness. - Huaming Yan; Monica Romero-Lopez; Hermann B. Frieboes; Christopher C. W. Hughes; John S. Lowengrub (IEEE Trans. Biomed. Eng., 2017)

Personalized Radiotherapy Planning for Glioma Using Multimodal Bayesian Model Calibration. - Jana Lipková; Panagiotis Angelikopoulos; Stephen Wu 001; Esther Alberts; Benedikt Wiestler; Christian Diehl; Christine Preibisch; Thomas Pyka; Stephanie Combs; Panagiotis E. Hadjidoukas; Koen Van Leemput; Petros Koumoutsakos; et al. (CoRR, 2018)

Efficient energy stable schemes for isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization. - Ying Chen; John S. Lowengrub; Jie Shen 001; Cheng Wang 015; Steven M. Wise (J. Comput. Phys., 2018)

A mass-conservative adaptive FAS multigrid solver for cell-centered finite difference methods on block-structured, locally-cartesian grids. - Wenqiang Feng; Zhenlin Guo; John S. Lowengrub; Steven M. Wise (J. Comput. Phys., 2018)

A Uniquely Solvable, Energy Stable Numerical Scheme for the Functionalized Cahn-Hilliard Equation and Its Convergence Analysis. - Wenqiang Feng; Zhen Guan; John S. Lowengrub; Cheng Wang 015; Steven M. Wise; Ying Chen (J. Sci. Comput., 2018)

Computation of a Shrinking Interface in a Hele-Shaw Cell. - Meng Zhao; Xiaofan Li 003; Wenjun Ying; Andrew Belmonte; John S. Lowengrub; Shuwang Li (SIAM J. Sci. Comput., 2018)

Boundary integral methods for dispersive equations, Airy flow and the modified Korteweg de Vries equation. - Mariano Franco-de-Leon; John S. Lowengrub (Adv. Comput. Math., 2019)

The Liver Tumor Segmentation Benchmark (LiTS). - Patrick Bilic; Patrick Ferdinand Christ; Eugene Vorontsov; Grzegorz Chlebus; Hao Chen 011; Qi Dou 001; Chi-Wing Fu; Xiao Han; Pheng-Ann Heng; Jürgen Hesser; Samuel Kadoury; Tomasz K. Konopczynski; et al. (CoRR, 2019)

Complex far-field geometries determine the stability of solid tumor growth with chemotaxis. - Min-Jhe Lu; Chun Liu 009; John S. Lowengrub; Shuwang Li (CoRR, 2019)

Morphological stability of an elastic tumor-host interface. - Emma Turian; Kai Liu; John S. Lowengrub; Shuwang Li (J. Comput. Appl. Math., 2019)

Efficient simulation of thermally fluctuating biopolymers immersed in fluids on 1-micron, 1-second scales. - Kai Liu; John S. Lowengrub; Jun Allard (J. Comput. Phys., 2019)

Hydrodynamics of transient cell-cell contact: The role of membrane permeability and active protrusion length. - Kai Liu; Brian Chu; Jay M. Newby; Elizabeth L. Read; John S. Lowengrub; Jun Allard (PLoS Comput. Biol., 2019)

Personalized Radiotherapy Design for Glioblastoma: Integrating Mathematical Tumor Models, Multimodal Scans, and Bayesian Inference. - Jana Lipková; Panagiotis Angelikopoulos; Stephen Wu 001; Esther Alberts; Benedikt Wiestler; Christian Diehl; Christine Preibisch; Thomas Pyka; Stephanie Combs; Panagiotis E. Hadjidoukas; Koen Van Leemput; Petros Koumoutsakos; et al. (IEEE Trans. Medical Imaging, 2019)

Higher-order accurate diffuse-domain methods for partial differential equations with Dirichlet boundary conditions in complex, evolving geometries. - Fei Yu; Zhenlin Guo; John S. Lowengrub (J. Comput. Phys., 2020)

A Multiscale Agent-Based Model of Ductal Carcinoma In Situ. - Joseph D. Butner; David Fuentes 001; Bulent Ozpolat; George A. Calin; Xiaobo Zhou 005; John S. Lowengrub; Vittorio Cristini; Zhihui Wang 008 (IEEE Trans. Biomed. Eng., 2020)

Stress generation, relaxation and size control in confined tumor growth. - Huaming Yan; Daniel Ramirez-Guerrero; John S. Lowengrub; Min Wu 012 (PLoS Comput. Biol., 2021)

Corrections to "A multiscale Agent-Based Model of Ductal Carcinoma in Situ". - Joseph D. Butner; David Fuentes 001; Bulent Ozpolat; George A. Calin; Xiaobo Zhou 005; John S. Lowengrub; Vittorio Cristini; Zhihui Wang 008 (IEEE Trans. Biomed. Eng., 2021)

Numerical study on viscous fingering using electric fields in a Hele-Shaw cell. - Meng Zhao; Pedro Anjos; John S. Lowengrub; Wenjun Ying; Shuwang Li (CoRR, 2022)

Phase field modeling and computation of vesicle growth or shrinkage. - Xiaoxia Tang; Shuwang Li; John S. Lowengrub; Steven M. Wise (CoRR, 2022)

Second order approximation for a quasi-incompressible Navier-Stokes Cahn-Hilliard system of two-phase flows with variable density. - Zhenlin Guo; Qing Cheng 003; Ping Lin; Chun Liu 009; John S. Lowengrub (J. Comput. Phys., 2022)

Nonlinear simulation of vascular tumor growth with chemotaxis and the control of necrosis. - Min-Jhe Lu; Wenrui Hao; Chun Liu 009; John S. Lowengrub; Shuwang Li (J. Comput. Phys., 2022)

Mathematical modeling of cancer immunotherapy for personalized clinical translation. - Joseph D. Butner; Prashant Dogra; Caroline Chung; Renata Pasqualini; Wadih Arap; John S. Lowengrub; Vittorio Cristini; Zhihui Wang 008 (Nat. Comput. Sci., 2022)

Spatial dynamics of feedback and feedforward regulation in cell lineages. - Peter Uhl; John S. Lowengrub; Natalia L. Komarova; Dominik Wodarz (PLoS Comput. Biol., 2022)

Correction: Stress generation, relaxation and size control in confined tumor growth. - Huaming Yan; Daniel Ramirez-Guerrero; John S. Lowengrub; Min Wu 012 (PLoS Comput. Biol., 2022)

Individualizing Glioma Radiotherapy Planning by Optimization of a Data and Physics Informed Discrete Loss. - Michal Balcerak; Ivan Ezhov; Petr Karnakov; Sergey Litvinov; Petros Koumoutsakos; Jonas Weidner; Ray Zirui Zhang; John S. Lowengrub; Benedikt Wiestler; Bjoern H. Menze (CoRR, 2023)

The Liver Tumor Segmentation Benchmark (LiTS). - Patrick Bilic; Patrick Ferdinand Christ; Hongwei Li 004; Eugene Vorontsov; Avi Ben-Cohen; Georgios Kaissis; Adi Szeskin; Colin Jacobs; Gabriel Efrain Humpire Mamani; Gabriel Chartrand; Fabian Lohöfer; Julian Walter Holch; et al. (Medical Image Anal., 2023)

Sharp-interface problem of the Ohta-Kawasaki model for symmetric diblock copolymers. - Amlan K. Barua; Ray Chew; Shuwang Li; John S. Lowengrub; Andreas Münch; Barbara Wagner (J. Comput. Phys., 2023)

BiLO: Bilevel Local Operator Learning for PDE inverse problems. - Ray Zirui Zhang; Xiaohui Xie; John S. Lowengrub (CoRR, 2024)

PIEZO1 regulates leader cell formation and cellular coordination during collective keratinocyte migration. - Jinghao Chen; Jesse R. Holt; Elizabeth L. Evans; John S. Lowengrub; Medha M. Pathak (PLoS Comput. Biol., 2024)

Personalized predictions of Glioblastoma infiltration: Mathematical models, Physics-Informed Neural Networks and multimodal scans. - Ray Zirui Zhang; Ivan Ezhov; Michal Balcerak; Andy Zhu; Benedikt Wiestler; Bjoern H. Menze; John S. Lowengrub (Medical Image Anal., 2025)

BiLO: Bilevel Local Operator Learning for PDE Inverse Problems. Part II: Efficient Uncertainty Quantification with Low-Rank Adaptation. - Ray Zirui Zhang; Christopher E. Miles; Xiaohui Xie; John S. Lowengrub (CoRR, 2025)