A Sharp Numerical Method for the Simulation of Stefan Problems with Convective Effects, E Bayat, R Egan, D Bochkov, A Sauret, F Gibou, Journal of Computational Physics, 111627 (2022).
Error-correcting neural networks for semi-Lagrangian advection in the level-set method, LÁ Larios-Cárdenas, F Gibou, Journal of Computational Physics, 111623 (2022).
A hybrid inference system for improved curvature estimation in the level-set method using machine learning, LÁ Larios-Cárdenas, F Gibou, Journal of Computational Physics, 111291 (2022).
Efficient calculation of fully resolved electrostatics around large biomolecules, R Chowdhury, R Egan, D Bochkov, F Gibou, Journal of Computational Physics 448, 110718 (2022).
Solving inverse-PDE problems with physics-aware neural networks, Samira Pakravan, Pouria Mistani, Miguel Aragon-Calvo, Frederic Gibou, Journal of Computational Physics 440, 110414 (2021).
Direct numerical simulation of incompressible flows on parallel octree grids, RaphaelEgan ArthurGuittet Fernando Temprano-Coleto TobinIsaac François J.Peaudecerf Julien R. Landel, Paolo Luzzatto-Fegiz Carsten Burstedded Frederic Gibou, Journal of Computational Physics 428, 110084 (2021).
A deep learning approach for the computation of curvature in the level-set method, LÁ Larios-Cárdenas, F Gibou, SIAM Journal on Scientific Computing 43, A1754-A1779 (2021).
xGFM: Recovering convergence of fluxes in the ghost fluid method, R Egan, F Gibou, Journal of Computational Physics 409, 109351 (2020).
Solving elliptic interface problems with jump conditions on Cartesian grids, D Bochkov, F Gibou, Journal of Computational Physics 407, 109269 (2020).
A theory for the slip and drag of superhydrophobic surfaces with surfactant, Julien R Landel, François J Peaudecerf, Fernando Temprano-Coleto, Frédéric Gibou, Raymond E Goldstein, Paolo Luzzatto-Fegiz, Journal of fluid mechanics 883 (2020).
PDE-Based Multidimensional Extrapolation of Scalar Fields over Interfaces with Kinks and High Curvatures, D Bochkov, F Gibou, SIAM Journal on Scientific Computing 42, A2344-A2359 (2020).
Slope selection in unstable multilayer growth in 1+1 dimensions: Step flow models with downward funneling, I Johnson, C Ratsch, F Gibou, D Margetis, Physical Review E 100 (5), 052802 (2019).
Sharp numerical simulation of incompressible two-phase flows, M Theillard, F Gibou, D Saintillan, Journal of Computational Physics 391, 91-118 (2019).
An examination of scaling behavior in unstable epitaxial mound growth via kinetic Monte Carlo simulations, JP Schneider, D Margetis, F Gibou, C Ratsch, Journal of Physics: Condensed Matter 31 (36), 365301 (2019).
Sharp interface approaches and deep learning techniques for multiphase flows, Frederic Gibou, David Hyde, Ronald Fedkiw, Journal of Computational Physics, 380, 442-463 (2019).
A parallel Voronoi-based approach for mesoscale simulations of cell aggregate electropermeabilization, P Mistani, A Guittet, C Poignard, F Gibou, Journal of Computational Physics 380, 48-64 (2019).
Solving Poisson-type equations with Robin boundary conditions on piecewise smooth interfaces, D Bochkov, F Gibou, Journal of Computational Physics 376, 1156-1198 (2019).
Towards a tensor network representation of complex systems , P Mistani, S Pakravan, F Gibou Sustainable Interdependent Networks II, 69-85 (2019).
Tensor Network Renormalization as an Ultra-calculus for Complex System Dynamics, P Mistani, S Pakravan, F Gibou Sustainable Interdependent Networks II, 87-106 (2019).
A review of level-set methods and some recent applications, Frederic Gibou, Ronald Fedkiw, Stanley Osher, Journal of Computational Physics, Volume 353, 82-109 (2018).
Level-set strategy for inverse DSA-lithography, Gaddiel Y. Ouaknin, Nabil Laachi, Kris Delaney, Glenn H. Fredrickson, Frederic Gibou, Journal of Computational Physics, Volume 375, 1159-1178 (2018).
Fast and scalable algorithms for constructing Solvent-Excluded Surfaces of large biomolecules, R. Egan, F. Gibou, Journal of Computational Physics, Volume 374, 91-120 (2018).
The island dynamics model on parallel quadtree grids, Pouria Mistani, Arthur Guittet, Daniil Bochkov, Joshua Schneider, Dionisios Margetis, Christian Ratsch, Frederic Gibou, Journal of Computational Physics, Volume 361, 150-166 (2018).
Poisson equations in irregular domains with Robin boundary conditions — Solver with second-order accurate gradients, Victoria Arias, Daniil Bochkov, Frederic Gibou, Journal of Computational Physics, Volume 365, 1-6 (2018).
Level-set simulations of soluble surfactant driven flows, Charles Cleret de Langavant, Arthur Guittet, Maxime Theillard, Fernando Temprano-Coleto, Frederic Gibou, Journal of Computational Physics, Volume 348, 271-297 (2017).
Geometric discretization of the multidimensional Dirac delta distribution – Application to the Poisson equation with singular source terms, Raphael Egan, Frederic Gibou, Journal of Computational Physics, Volume 346, 71-90 (2017).
Functional level-set derivative for a polymer self consistent field theory Hamiltonian, Gaddiel Ouaknin, Nabil Laachi, Daniil Bochkov, Kris Delaney, Glenn H. Fredrickson, Frederic Gibou, Journal of Computational Physics, Volume 345, 207-223 (2017).
A Voronoi Interface approach to cell aggregate electropermeabilization, A. Guittet, C. Poignard, F. Gibou, Journal of Computational Physics, Volume 332, 143-159 (2017).
Parallel level-set methods on adaptive tree-based grids, M. Mirzadeh, A. Guittet, C. Burstedde, F. Gibou, Journal of Computational Physics, Volume 322, 345-364 (2016).
Hybrid massively parallel fast sweeping method for static Hamilton–Jacobi equations, M. Detrixhe, F. Gibou, Journal of Computational Physics, Volume 322, 199-223 (2016).
Self-consistent field theory simulations of polymers on arbitrary domains, G. Ouaknin, N. Laachi, K. Delaney, G.H. Fredrickson, F. Gibou, Journal of Computational Physics, Volume 327, 168-185 (2016).
On two-phase flow solvers in irregular domains with contact line, M. Lepilliez, E.R. Popescu, F. Gibou, S. Tanguy, Journal of Computational Physics, Volume 321, 1217-1251 (2016).
A stable projection method for the incompressible Navier–Stokes equations on arbitrary geometries and adaptive Quad/Octrees, A. Guittet, M. Theillard, F. Gibou, Journal of Computational Physics, Volume 292, 215-238 (2015).
Solving elliptic problems with discontinuities on irregular domains – the Voronoi Interface Method, A. Guittet, M. Lepilliez, S. Tanguy, F. Gibou, Journal of Computational Physics, Volume 298, 747-765 (2015).
A conservative discretization of the Poisson–Nernst–Planck equations on adaptive Cartesian grids, M. Mirzadeh, F. Gibou, Journal of Computational Physics, Volume 274, 633-653 (2014).
Enhanced Charging Kinetics of Porous Electrodes: Surface Conduction as a Short Circuit Mechanism , M. Mirzadeh, F. Gibou, and T. Squires, Phys. Rev. Lett., 113, 097701, (2014).
High resolution sharp computational methods for elliptic and parabolic problems in complex geometries, F. Gibou, C. Min and R. Fedkiw, Journal of Scientific Computing, Volume 54, 369-413, (2013).
A level set approach for diffusion and Stefan-type problems with Robin boundary conditions on quadtree/octree adaptive Cartesian grids, J. Papac, A. Helgadottir, C. Ratsch and F. Gibou, Journal of Computational Physics, Volume 233, 241-261, (2013).
A parallel fast sweeping method for the Eikonal equation, M. Detrixhe, F. Gibou and C. Min, Journal of Computational Physics, Volume 237, Pages 46-55, (2013).
Minimum Energy Desynchronizing Control for Coupled Neurons, A. Nabi, M. Mirzadeh, F. Gibou, and J. Moehlis, J. Comput. Neurosci., Volume 34, Pages 259-271, (2013).
A second-order sharp numerical method for solving the linear elasticity equations on irregular domains and adaptive grids – Application to shape optimization, M. Theillard, L. Fokoua Djodom, J.-L. Vié and F. Gibou, Journal of Computational Physics, Volume 233, Pages 430-448, (2013).
A Multigrid Method on Non-Graded Adaptive Octree and Quadtree Cartesian Grids, M. Theillard, C. Rycroft and F. Gibou, Journal of Scientific Computing, Volume 55, Pages 1-15, (2013).
On the performance of a simple parallel implementation of the ILU-PCG for the Poisson equation on irregular domains, F. Gibou and C. Min, Journal of Computational Physics, Volume 231, pages 4531-4536, (2012).
Efficient symmetric positive definite second-order accurate monolithic solver for fluid/solid interactions, F. Gibou and C. Min, Journal of Computational Physics, Volume 231, Pages 3246-3263, (2012).
A local level-set method using a hash table data structure, E. Brun, A. Guittet and F. Gibou, Journal of Computational Physics, Volume 231, Pages 2528-2536, (2012).
Minimum Energy Spike Randomization for Neurons, A. Nabi, M. Mirzadeh, F. Gibou, and J. Moehlis, Proceedings of the 2012 American Control Conference, 4751-4756, (2012).
Simulations of a stretching bar using a plasticity model from the shear transformation zone theory, C. H. Rycroft and F. Gibou, Journal of Computational Physics, Volume 231, Pages 2155-2179, (2012).
An Adaptive, Finite Difference Solver for the Non-linear Poisson-Boltzmann Equation with Applications to Biomolecular Computations, M. Mirzadeh, M. Theillard, A. Helgadottir, D. Boy, and F. Gibou, Commun. Comput. Phys., (2012).
A Poisson–Boltzmann solver on irregular domains with Neumann or Robin boundary conditions on non-graded adaptive grid, A Helgadóttir and F. Gibou, Journal of Computational Physics, Volume 230, Pages 3830-3848, (2011).
A second-order discretization of the nonlinear Poisson–Boltzmann equation over irregular geometries using non-graded adaptive Cartesian grids, M. Mirzadeh, M. Theillard and F. Gibou, Journal of Computational Physics, Volume 230, Pages 2125-2140, (2011).
Efficient symmetric discretization for the Poisson, heat and Stefan-type problems with Robin boundary conditions, J. Papac, F. Gibou and C. Ratsch, Journal of Computational Physics, Volume 229, Pages 875-889, (2010).
On the Length and Area Regularization for Multiphase Level Set Segmentation, L. Bertelli, S. Chadrasekaran, F. Gibou and B.S. Manjunath, IJCV, Volume 90, Pages 267-, (2010).
A numerical scheme for the Stefan problem on adaptive Cartesian grids with supralinear convergence rate, H. Chen, C. Min and F. Gibou, Journal of Computational Physics, Volume 228, Pages 5803-5818, (2009).
An efficient fluid–solid coupling algorithm for single-phase flows, Y. T. Ng, C. Min and F. Gibou, Journal of Computational Physics, Volume 228, Pages 8807-8829, (2009).
Guidelines for Poisson Solvers on Irregular Domains with Dirichlet Boundary Conditions Using the Ghost Fluid Method, Y.-T. Ng, H. Chen, C. Min and F. Gibou, Journal of Scientific Computing, Volume 41, Pages 300-320, (2009).
Robust second-order accurate discretizations of the multi-dimensional Heaviside and Dirac delta functions, C. Min and F. Gibou, Journal of Computational Physics, Volume 227, Pages 9686-9695, (2008).
A Variational Framework for Multi-Region Pairwise Similarity-Based Image Segmentation, L. Bertelli, B. Sumengen, B.S. Manjunath and F. Gibou, Pattern Analysis and Machine Intelligence, Volume 30, Pages 1400-1414, (2008).
Second-order accurate computation of curvatures in a level set framework using novel high-order reinitialization schemes, A Du-Chene, C. Min and F. Gibou, Journal of Scientific Computing, Volume 35, Pages 114-131, (2008).
A level set based sharp interface method for the multiphase incompressible Navier–Stokes equations with phase change, F. Gibou, L. Chen, D. Nguyen and S. Banerjee, Journal of Computational Physics, Volume 222, Pages 536-555, (2007).
A second order accurate level set method on non-graded adaptive cartesian grids, C. Min and F. Gibou, Journal of Computational Physics, Volume 225, Pages 300-3214, (2007).
Geometric integration over irregular domains with application to level-set methods, C. Min and F. Gibou, Journal of Computational Physics, Volume 226, Pages 1432-1443, (2007).
Finite Difference Schemes for Incompressible Flows on Non-Graded Adaptive Cartesian Grids, F. Gibou, C. Min and H. Ceniceros, Fluid Dynamics and Materials Processing, Volume 3, Pages 37-48, (2007).
A Supra-Convergent Finite Difference Scheme for the Poisson and Heat Equations on Irregular Domains and Non-Graded Adaptive Cartesian Grids, H. Chen, C. Min and F. Gibou, Journal of Scientific Computing, Volume 31, Pages 19-60, (2007).
A supra-convergent finite difference scheme for the variable coefficient Poisson equation on non-graded grids, C. Min, F. Gibou and Hector D. Ceniceros, Journal of Computational Physics, Volume 218, Pages 123-140, (2006).
A second order accurate projection method for the incompressible Navier–Stokes equations on non-graded adaptive grids, C. Min and F. Gibou, Journal of Computational Physics, Volume 219, Pages 912-929, (2006).
A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains, with applications to the Stefan problem, F. Gibou and R. Fedkiw, Journal of Computational Physics, Volume 202, Pages 577-601, (2005).
Fast Hybrid k-Means Level Set Algorithm For Segmentation, F. Gibou and R. Fedkiw, Stanford Technical Report, November 2002. Also in the proceeding of the 4th Annual Hawaii International Conference on Statistics and Mathematics., (2005)
Partial Differential Equation based Segmentation for Radiotherapy Treatment Planning, F. Gibou, D. Levy, C. Cardenas, P. Liu and A. Boyer, Mathematical Biosciences and Engineering, Volume 2, Pages 209-226, (2005).
Simulating Water and Smoke with an Octree Data Structure, F. Losasso, F. Gibou and R. Fedkiw, SIGGRAPH 2004, ACM TOG 23, Pages 457-462, (2004).
Capture Numbers in Rate Equations and Scaling Laws for Epitaxial Growth, F. Gibou, C. Ratsch, and R. Caflisch, Physical Review B, Volume 67, Pages 155403-, (2003).
A Level Set Approach for the Numerical Simulation of Dendritic Growth, F. Gibou, R. Fedkiw, R. Caflisch and S. Osher, Journal of Scientific Computing, Volume 19, Pages 183-199, (2003).
Singularities and Spatial Fluctuations in Submonolayer Epitaxy, D. Vvdensky, C. Ratsch, F. Gibou and R. Vardavas, Physical Revue Letters, Volume 90, 189601, (2003).
Using the Particle Level Set Method and a Second Order Accurate Pressure Boundary Condition for Free Surface Flows, D. Enright, D. Nguyen, F. Gibou and R. Fedkiw, Proc. of the 4th ASME-JSME Joint Fluids Eng. Conf., FEDSM2003-45144, edited by M. Kawahashi and A. Ogut and Y. Tsuji, pp. 1-6, Honolulu, HI, (2003).
A Second-Order-Accurate Symmetric Discretization of the Poisson Equation on Irregular Domains, F. Gibou, R. P. Fedkiw, L.-T. Cheng and M. Kang, Journal of Computational Physics, Volume 176, Pages 205-227, (2002).
Level-Set Method for Island Dynamics in Epitaxial Growth, C. Ratsch, M. Gyure, R. Caflisch, F. Gibou, M. Petersen, M. Kang, J. Garcia and D. Vvedensky, Physical Review B, Volume 65, 195403, (2002).
A Fully Conservative Ghost Fluid Method & Stiff Detonation Waves, D. Nguyen, F. Gibou and R. Fedkiw, 12th Int. Detonation Symposium, San Diego, CA, (2002).