A three-dimensional model-based segmentation system for the radiation oncology treatment plannin. - Carlos Cardenas; Frédéric Gibou; Doron Levy; Arthur Boyer (CARS, 2003)

A Level Set Approach for the Numerical Simulation of Dendritic Growth. - Frédéric Gibou; Ronald Fedkiw; Russel E. Caflisch; Stanley J. Osher (J. Sci. Comput., 2003)

Simulating water and smoke with an octree data structure. - Frank Losasso; Frédéric Gibou; Ronald Fedkiw (ACM Trans. Graph., 2004)

A second order accurate projection method for the incompressible Navier-Stokes equations on non-graded adaptive grids. - Chohong Min; Frédéric Gibou (J. Comput. Phys., 2006)

A supra-convergent finite difference scheme for the variable coefficient Poisson equation on non-graded grids. - Chohong Min; Frédéric Gibou; Héctor D. Ceniceros (J. Comput. Phys., 2006)

A level set based sharp interface method for the multiphase incompressible Navier-Stokes equations with phase change. - Frédéric Gibou; Liguo Chen; Duc Nguyen; Sanjoy Banerjee (J. Comput. Phys., 2007)

Geometric integration over irregular domains with application to level-set methods. - Chohong Min; Frédéric Gibou (J. Comput. Phys., 2007)

A second order accurate level set method on non-graded adaptive cartesian grids. - Chohong Min; Frédéric Gibou (J. Comput. Phys., 2007)

A Supra-Convergent Finite Difference Scheme for the Poisson and Heat Equations on Irregular Domains and Non-Graded Adaptive Cartesian Grids. - Han Chen; Chohong Min; Frédéric Gibou (J. Sci. Comput., 2007)

Reference-based probabilistic segmentation as non-rigid registration using Thin Plate Splines. - Luca Bertelli; Pratim Ghosh; B. S. Manjunath; Frédéric Gibou (ICIP, 2008)

Robust second-order accurate discretizations of the multi-dimensional Heaviside and Dirac delta functions. - Chohong Min; Frédéric Gibou (J. Comput. Phys., 2008)

Second-Order Accurate Computation of Curvatures in a Level Set Framework Using Novel High-Order Reinitialization Schemes. - Antoine du Chéné; Chohong Min; Frédéric Gibou (J. Sci. Comput., 2008)

A Variational Framework for Multiregion Pairwise-Similarity-Based Image Segmentation. - Luca Bertelli; Baris Sumengen; B. S. Manjunath; Frédéric Gibou (IEEE Trans. Pattern Anal. Mach. Intell., 2008)

A numerical scheme for the Stefan problem on adaptive Cartesian grids with supralinear convergence rate. - Han Chen; Chohong Min; Frédéric Gibou (J. Comput. Phys., 2009)

An efficient fluid-solid coupling algorithm for single-phase flows. - Yen Ting Ng; Chohong Min; Frédéric Gibou (J. Comput. Phys., 2009)

Guidelines for Poisson Solvers on Irregular Domains with Dirichlet Boundary Conditions Using the Ghost Fluid Method. - Yen Ting Ng; Han Chen; Chohong Min; Frédéric Gibou (J. Sci. Comput., 2009)

On the Length and Area Regularization for Multiphase Level Set Segmentation. - Luca Bertelli; Shivkumar Chandrasekaran; Frédéric Gibou; B. S. Manjunath (Int. J. Comput. Vis., 2010)

Efficient symmetric discretization for the Poisson, heat and Stefan-type problems with Robin boundary conditions. - Joseph Papac; Frédéric Gibou; Christian Ratsch (J. Comput. Phys., 2010)

A Poisson-Boltzmann solver on irregular domains with Neumann or Robin boundary conditions on non-graded adaptive grid. - Ásdís Helgadóttir; Frédéric Gibou (J. Comput. Phys., 2011)

A second-order discretization of the nonlinear Poisson-Boltzmann equation over irregular geometries using non-graded adaptive Cartesian grids. - Mohammad Mirzadeh; Maxime Theillard; Frédéric Gibou (J. Comput. Phys., 2011)

Minimum energy spike randomization for neurons. - Ali Nabi; Mohammad Mirzadeh; Frédéric Gibou; Jeff Moehlis (ACC, 2012)

A local level-set method using a hash table data structure. - Emmanuel Brun; Arthur Guittet; Frédéric Gibou (J. Comput. Phys., 2012)

Efficient symmetric positive definite second-order accurate monolithic solver for fluid/solid interactions. - Frédéric Gibou; Chohong Min (J. Comput. Phys., 2012)

On the performance of a simple parallel implementation of the ILU-PCG for the Poisson equation on irregular domains. - Frédéric Gibou; Chohong Min (J. Comput. Phys., 2012)

Simulations of a stretching bar using a plasticity model from the shear transformation zone theory. - Chris H. Rycroft; Frédéric Gibou (J. Comput. Phys., 2012)

Minimum energy desynchronizing control for coupled neurons. - Ali Nabi; Mohammad Mirzadeh; Frédéric Gibou; Jeff Moehlis (J. Comput. Neurosci., 2013)

A parallel fast sweeping method for the Eikonal equation. - Miles Detrixhe; Frédéric Gibou; Chohong Min (J. Comput. Phys., 2013)

A level set approach for diffusion and Stefan-type problems with Robin boundary conditions on quadtree/octree adaptive Cartesian grids. - Joseph Papac; Ásdís Helgadóttir; Christian Ratsch; Frédéric Gibou (J. Comput. Phys., 2013)

A second-order sharp numerical method for solving the linear elasticity equations on irregular domains and adaptive grids - Application to shape optimization. - Maxime Theillard; Landry Fokoua Djodom; Jean-Léopold Vié; Frédéric Gibou (J. Comput. Phys., 2013)

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries. - Frédéric Gibou; Chohong Min; Ronald Fedkiw (J. Sci. Comput., 2013)

A Multigrid Method on Non-Graded Adaptive Octree and Quadtree Cartesian Grids. - Maxime Theillard; Chris H. Rycroft; Frédéric Gibou (J. Sci. Comput., 2013)

A conservative discretization of the Poisson-Nernst-Planck equations on adaptive Cartesian grids. - Mohammad Mirzadeh; Frédéric Gibou (J. Comput. Phys., 2014)

Solving elliptic problems with discontinuities on irregular domains - the Voronoi Interface Method. - Arthur Guittet; Mathieu Lepilliez; Sébastien Tanguy; Frédéric Gibou (J. Comput. Phys., 2015)

A stable projection method for the incompressible Navier-Stokes equations on arbitrary geometries and adaptive Quad/Octrees. - Arthur Guittet; Maxime Theillard; Frédéric Gibou (J. Comput. Phys., 2015)

A Sharp Computational Method for the Simulation of the Solidification of Binary Alloys. - Maxime Theillard; Frédéric Gibou; Tresa Pollock (J. Sci. Comput., 2015)

Hybrid massively parallel fast sweeping method for static Hamilton-Jacobi equations. - Miles Detrixhe; Frédéric Gibou (J. Comput. Phys., 2016)

On two-phase flow solvers in irregular domains with contact line. - Mathieu Lepilliez; Elena Roxana Popescu; Frédéric Gibou; Sébastien Tanguy (J. Comput. Phys., 2016)

Parallel level-set methods on adaptive tree-based grids. - Mohammad Mirzadeh; Arthur Guittet; Carsten Burstedde; Frédéric Gibou (J. Comput. Phys., 2016)

Self-consistent field theory simulations of polymers on arbitrary domains. - Gaddiel Ouaknin; Nabil Laachi; Kris T. Delaney; Glenn H. Fredrickson; Frédéric Gibou (J. Comput. Phys., 2016)

A Fast Eulerian Approach for Computation of Global Isochrons in High Dimensions. - Miles Detrixhe; Marion Doubeck; Jeff Moehlis; Frédéric Gibou (SIAM J. Appl. Dyn. Syst., 2016)

Geometric discretization of the multidimensional Dirac delta distribution - Application to the Poisson equation with singular source terms. - Raphael Egan; Frédéric Gibou (J. Comput. Phys., 2017)

A Voronoi Interface approach to cell aggregate electropermeabilization. - Arthur Guittet; Clair Poignard; Frédéric Gibou (J. Comput. Phys., 2017)

Level-set simulations of soluble surfactant driven flows. - Charles Cleret de Langavant; Arthur Guittet; Maxime Theillard; Fernando Temprano-Coleto; Frédéric Gibou (J. Comput. Phys., 2017)

Functional level-set derivative for a polymer self consistent field theory Hamiltonian. - Gaddiel Ouaknin; Nabil Laachi; Daniil Bochkov; Kris T. Delaney; Glenn H. Fredrickson; Frédéric Gibou (J. Comput. Phys., 2017)

Poisson equations in irregular domains with Robin boundary conditions - Solver with second-order accurate gradients. - Victoria Arias; Daniil Bochkov; Frédéric Gibou (J. Comput. Phys., 2018)

Fast and scalable algorithms for constructing Solvent-Excluded Surfaces of large biomolecules. - Raphael Egan; Frédéric Gibou (J. Comput. Phys., 2018)

A review of level-set methods and some recent applications. - Frédéric Gibou; Ronald Fedkiw; Stanley J. Osher (J. Comput. Phys., 2018)

The island dynamics model on parallel quadtree grids. - Pouria Mistani; Arthur Guittet; Daniil Bochkov; Joshua Schneider 002; Dionisios Margetis; Christian Ratsch; Frédéric Gibou (J. Comput. Phys., 2018)

Level-set strategy for inverse DSA-lithography. - Gaddiel Ouaknin; Nabil Laachi; Kris T. Delaney; Glenn H. Fredrickson; Frédéric Gibou (J. Comput. Phys., 2018)

Multidimensional Extrapolation over Interfaces with Kinks and Regions of High Curvatures. - Daniil Bochkov; Frédéric Gibou (CoRR, 2019)

Solving Poisson-type equations with Robin boundary conditions on piecewise smooth interfaces. - Daniil Bochkov; Frédéric Gibou (J. Comput. Phys., 2019)

Sharp interface approaches and deep learning techniques for multiphase flows. - Frédéric Gibou; David Hyde 001; Ron Fedkiw (J. Comput. Phys., 2019)

A parallel Voronoi-based approach for mesoscale simulations of cell aggregate electropermeabilization. - Pouria Mistani; Arthur Guittet; Clair Poignard; Frédéric Gibou (J. Comput. Phys., 2019)

Sharp numerical simulation of incompressible two-phase flows. - Maxime Theillard; Frédéric Gibou; David Saintillan (J. Comput. Phys., 2019)

A fractional stochastic theory for interfacial polarization of cell aggregates. - Pouria A. Mistani; Samira Pakravan; Frédéric Gibou (CoRR, 2020)

Solving elliptic interface problems with jump conditions on Cartesian grids. - Daniil Bochkov; Frédéric Gibou (J. Comput. Phys., 2020)

xGFM: Recovering convergence of fluxes in the ghost fluid method. - Raphael Egan; Frédéric Gibou (J. Comput. Phys., 2020)

PDE-Based Multidimensional Extrapolation of Scalar Fields over Interfaces with Kinks and High Curvatures. - Daniil Bochkov; Frédéric Gibou (SIAM J. Sci. Comput., 2020)

Level-Set Curvature Neural Networks: A Hybrid Approach. - Luis Ángel Larios Cárdenas; Frédéric Gibou (CoRR, 2021)

Direct numerical simulation of incompressible flows on parallel Octree grids. - Raphael Egan; Arthur Guittet; Fernando Temprano-Coleto; Tobin Isaac; François Peaudecerf; Julien R. Landel; Paolo Luzzatto-Fegiz; Carsten Burstedde; Frédéric Gibou (J. Comput. Phys., 2021)

Solving inverse-PDE problems with physics-aware neural networks. - Samira Pakravan; Pouria A. Mistani; Miguel A. Aragon-Calvo; Frédéric Gibou (J. Comput. Phys., 2021)

A Deep Learning Approach for the Computation of Curvature in the Level-Set Method. - Luis Ángel Larios Cárdenas; Frédéric Gibou (SIAM J. Sci. Comput., 2021)

Neuro-symbolic partial differential equation solver. - Pouria Mistani; Samira Pakravan; Rajesh Ilango; Sanjay Choudhry; Frédéric Gibou (CoRR, 2022)

A sharp numerical method for the simulation of Stefan problems with convective effects. - Elyce Bayat; Raphael Egan; Daniil Bochkov; Alban Sauret; Frédéric Gibou (J. Comput. Phys., 2022)

A hybrid inference system for improved curvature estimation in the level-set method using machine learning. - Luis Ángel Larios Cárdenas; Frédéric Gibou (J. Comput. Phys., 2022)

Error-correcting neural networks for semi-Lagrangian advection in the level-set method. - Luis Ángel Larios Cárdenas; Frédéric Gibou (J. Comput. Phys., 2022)

Efficient calculation of fully resolved electrostatics around large biomolecules. - Rochishnu Chowdhury; Raphael Egan; Daniil Bochkov; Frédéric Gibou (J. Comput. Phys., 2022)

Error-Correcting Neural Networks for Two-Dimensional Curvature Computation in the Level-set Method. - Luis Ángel Larios Cárdenas; Frédéric Gibou (J. Sci. Comput., 2022)

Machine learning algorithms for three-dimensional mean-curvature computation in the level-set method. - Luis Ángel Larios Cárdenas; Frédéric Gibou (J. Comput. Phys., 2023)

JAX-DIPS: Neural bootstrapping of finite discretization methods and application to elliptic problems with discontinuities. - Pouria A. Mistani; Samira Pakravan; Rajesh Ilango; Frédéric Gibou (J. Comput. Phys., 2023)

A numerical method for sharp-interface simulations of multicomponent alloy solidification. - Daniil Bochkov; Tresa Pollock; Frédéric Gibou (J. Comput. Phys., 2023)

Optimal control for stochastic neural oscillators. - Faranak Rajabi; Frédéric Gibou; Jeff Moehlis (Biol. Cybern., 2025)

CASL-HJX: A Comprehensive Guide to Solving Deterministic and Stochastic Hamilton-Jacobi Equations. - Faranak Rajabi; Jacob Fingerman; Andrew Wang; Jeff Moehlis; Frédéric Gibou (CoRR, 2025)