1. A. Caboussat, D. Gourzoulidis, M. Picasso, An anisotropic adaptive method for the numerical approximation of orthogonal maps,  J. Comput. Appl. Math, submitted, 2020.

  1. A. Caboussat, D. Gourzoulidis, M. Picasso. An adaptive method for the numerical solution of a 2D Monge-Ampère equation. Proceedings of the International Conference on Adaptive Modeling and Simulation ADMOS 2021, to appear, 2021.
  2. A. Caboussat, J. Hess, A. Masserey, M. Picasso. Numerical simulation of temperature-driven free surface flows, with application to laser surface melting. Proceedings of the 14th World Congress on Computational Mechanics (WCCM) and ECCOMAS Congress. F. Chinesta, R. Abgrall, O. Allix and M. Kaliske Editors, 2021. (DOI : 0.23967/wccmeccomas.2020.245)
  3. A. Caboussat, D. Gourzoulidis, A second order time stepping method for the approximation of a parabolic 2D Monge-Ampère equation, Proceedings of Numerical Mathematics and Advanced Applications ENUMATH 2019, F. Vermolen, C. Vuik editors, Lecture Notes in Computational Science and Engineering 139, Springer, 2021
  4. A. Caboussat, Least-squares/relaxation method for the numerical solution of a 2D Pucci’s equation, Methods and Applications of Analysis, Vol. 26, No. 2, pages 113-132, 2019.
  5. A. Caboussat, R. Glowinski, D. Gourzoulidis, M. Picasso, Numerical Approximation of Orthogonal Maps,  SIAM J. Sci. Comput., Volume 41, pages B1341–B1367, 2019.
  6. A. Caboussat, J. Hess, A. Masserey, M. Picasso, A numerical model for the simulation of shallow laser surface melting, Proceedings of the II International Conference on Simulation for Additive Manufacturing Sim-AM 2019, 11-13 September, 2019, Pavia, Italy. F. Auricchio, E. Rank, P. Steinmann, S. Kollmannsberger and S. Morganti (Eds), pages 286–296, 2019.
  7. S. Boyaval, A. Caboussat, A. Mrad, M. Picasso, G. Steiner, A semi-Lagrangian splitting method for the numerical simulation of sediment transport with free surface flows, Computers and Fluids, Volume 172, pages 384–396, 2018.
  8. A. Caboussat, R. Glowinski, D. Gourzoulidis, A Least-Squares/Relaxation Method for the Numerical Solution of the Three- Dimensional Elliptic Monge-Ampère Equation, J. Sci. Comp., 77(1), pages 53–78, 2018.    
  9. A. Caboussat, R. Glowinski, An alternating direction method of multipliers for the numerical solution of a partial differential equation involving the Jacobian determinant , SIAM J. Sci. Comp., Volume 40(1), pages A52-A80, 2018.
  10. A. Bonito, A. Caboussat, M. Picasso. Operator Splitting Algorithms for Free Surface Flows: Application to Extrusion Processes. Splitting methods in communication, imaging, science and engineering, Springer, pages 677–729, 2016.
  11. A. Caboussat, R. Glowinski, A Penalty-Regularization-Operator Splitting Method for the Numerical Solution of a Scalar Eikonal Equation, Chinese Annals of Mathematics, Series B, Volume 36, Issue 5, pages 659–688, 2015.
  12. A. Caboussat, R. Glowinski, T.-W. Pan, On the Numerical Solution of Some Eikonal Equations: An Elliptic Solver Approach, Chinese Annals of Mathematics, Series B, Volume 36, Issue 5, pages 689–702, 2015.
  13. A. Caboussat, R. Glowinski, A Numerical Algorithm for a Fully Nonlinear PDE Involving the Jacobian Determinant, Numerical Mathematics and advanced applications ENUMATH 2013. Lecture Notes in Computer Science and Engineering, Springer, Volume 103, pages 143–151, 2015.
  14. N. James, S. Boyaval, A. Caboussat, M. Picasso, Numerical simulation of 3D free surface flows, with multiple incompressible immiscible phases. Applications to impulse waves, Int. J. Numer. Meth. Fluids,Volume 76, Issue 12, pages 1004–1024, 2014.
  15. A. Caboussat, N. James, S. Boyaval, M. Picasso, Numerical simulation of free surface flows, with multiple liquid phases, Proceedings of the 11th World Congress on Computational Mechanics (WCCM XI), 5th European Conference on Computational Mechanics (ECCM V) and 6th European Conference on Computational Fluid Dynamics (ECFD VI), E. Onate, J. Oliver and A. Huerta (Eds), pages 5381–5391, 2014.
  16. A. Caboussat. On the numerical solution of the Dirichlet problem for the elliptic ‘sigma-2’ equation, “Modeling, Simulation and Optimization in Science and Technology”, ECCOMAS series, Fitzgibbon et al Eds., 23–40, Springer, 2014.
  17. A. Caboussat, R. Glowinski, D. C. Sorensen. On the least-squares solution of the Dirichlet problem for the elliptic Monge-Ampère equation in dimension two, ESAIM: Control, Optimization and Calculus of Variations, 19(3), 780–810, 2013. https://doi.org/10.1051/cocv/2012033
  18. A. Caboussat, S. Boyaval, A. Masserey. On the Modeling and Simulation of Non-Hydrostatic Dam Break Flows , Comp. Vis. Science 14(8), 401–417, 2013.
  19. A. Caboussat, R. Glowinski. Regularization methods for the Numerical Solution of the Divergence Equation div u = f , J. Comp. Math, 30(4), 354–380, 2012.
  20. A. Caboussat, P. Clausen, J. Rappaz. Numerical Simulation of Two-Phase Flow with Interface Tracking by Adaptive Eulerian Grid Subdivision, Mathematical and Computer Modelling, 55, 490–504, 2012.
  21. A. Caboussat, L. Kiss, J. Rappaz, K. Vekony, A. Perron, S. Renaudier, O. Martin. Large Gas Bubbles under the Anodes of Aluminum Electrolysis Cells, in Light Metals (Ed S.J.Lindsay), John Wiley and Sons, Inc., 2011.
  22. A. Caboussat. Mathematical Modeling of Atmospheric Flow and Numerical Computation of Convex Envelopes, Math. Model. Nat. Phenom., 6(5), 44–66, 2011.
  23. A. Caboussat, G. Jouvet, M. Picasso, J. Rappaz. Numerical Algorithms for Free Surface Flow, in ‘Computational Fluid Dynamics’ (Ed. F. Magoules), 263–326, CRC Press, Taylor and Francis, 2011.
  24. A. Caboussat. Primal-Dual Interior-Point Method for Thermodynamic Gas-Particle Partitioning, Comp. Optim. and Appl., 48(3), 717–745, 2011. (DOI: 10.1007/s10589-009-9262-5)
  25. A. Caboussat, R. Glowinski, A. Leonard. Looking for the Best Constant in a Sobolev Inequality : A Numerical Approach , Calcolo, 47(4), 211–238, 2010.
  26. A. Caboussat, C. Landry, J. Rappaz. Optimization Problem Coupled with Differential Equations: A Numerical Algorithm mixing an Interior-Point Method and Event Detection, J. Optim. Theory. Appl. 147(1), 141–156, 2010.
  27. A. Caboussat, R. Glowinski. Numerical Methods for the Vector-Valued Solutions of Non-Smooth Eigenvalue Problems, J. Sci. Comp., 45(1-3), 64–89, 2010.
  28. A. Caboussat, J. Rappaz. Numerical Simulation of Bubbles under an Inclined Plane: Application to Aluminum Electrolysis , EPFL-MATHICSE technical report number 03.2010, 2010.
  29. A. Caboussat, R. Glowinski. Numerical solution of a variational problem arising in stress analysis: the vector case, Discrete and Continuous Dynamical Systems, Series A, 27(4), 1447–1472, 2010.
  30. A. Caboussat, G. K. Miers. Numerical Approximation of Electromagnetic Signals Arising in the Evaluation of Geological Formations, Computers and Mathematics with Applications, 58, 338–351, 2010.
  31. K. Nguyen, A. Caboussat, D. Dabdub. Mass Conservative, Positive Definite Integrator for Atmospheric Chemical Dynamics, Atmospheric Environment, 43(40), 6287–6295, 2009.
  32. A. Caboussat, A. Leonard. Numerical Solution and Fast-Slow Decomposition of a Population of Weakly Coupled Systems, DCDS Supplements, 2009(Special), 123–132, 2009.
  33. C. Landry, A. Caboussat, E. Hairer. Solving Optimization-Constrained Differential Equations with Discontinuity Points, with Application to Atmospheric Chemistry, SIAM J. Sci. Comp., 31(5), 3806–3826, 2009.
  34. A. Caboussat, R. Glowinski, V. Pons. An Augmented Lagrangian Approach to the Numerical Solution of a Non-Smooth Eigenvalue Problem, J. Numer. Math., 17(1), 3–26, 2009. https://doi.org/10.1515/JNUM.2009.002
  35. A. Caboussat, R. Glowinski. Numerical Solution of a Non-Smooth Variational Problem Arising in Stress Analysis : The Scalar Case, Int. J. Numerical Analysis and Modeling 6(3), 402–419, 2009.
  36. A. Caboussat, R. Glowinski, V. Pons. Numerical Methods for Non-Smooth L1 Optimization : Applications to Free Surface Flows and Image Denoising, Int. J. Numerical Analysis and Modeling 6(3), 355–374, 2009.
  37. A. Caboussat, R. Glowinski. A Numerical Method for a Non-Smooth Advection-Diffusion Problem Arising in Sand Mechanics, Com. Pure. Appl. Anal 8(1), 161–178, 2009.
  38. A. Caboussat, C. Landry. A second order scheme for solving optimization-constrained differential equations with discontinuities, in Numerical Mathematics and Advanced Applications, pages 761–768, Springer Verlag, Berlin, 2008. Proceedings of Enumath 2007, the 7th European Conference on Numerical Mathematics and Advanced Applications, Graz, Austria, September 2007.
  39. A. Caboussat, M. M. Francois, R. Glowinski, D. B. Kothe, J. M. Sicilian. A Numerical Method for Interface Reconstruction of Triple Points within a Volume Tracking Algorithm, Los Alamos National Laboratory technical report LA-UR-07-7960, Mathematical and Computer Modelling, 48, pages 1957–1971, 2008.
  40. A. Bonito, A. Caboussat, M. Picasso and J. Rappaz. A Numerical Method for Fluid Flows with Complex Free Surfaces, in Partial Differential Equations: Modeling and Simulation, pages 187–208, R. Glowinski and P. Neittaanmaki eds., Springer, 2008.
  41. A. Caboussat, R. Glowinski. Modeling and Computation of the Shape of a Compressed Axisymmetric Gas Bubble, J. Numer. Math., 16(2), pages 107–117, 2008.
  42. A. Caboussat, C. Landry. Dynamic Optimization and Event Location in Atmospheric Chemistry , Proc. Appl. Math. Mech. (PAMM), 7(1), pages 2020035-2020036, 2007. Special Issue: Sixth International Congress on Industrial Applied Mathematics (ICIAM07).
  43. A. Caboussat, A. Leonard. Numerical Method for a Dynamic Optimization Problem arising in the Modeling of a Population of Aerosol Particles, C. R. Acad. Sci. Paris, 346(11-12), pages 677–680, 2008.
  44. N. R. Amundson, A. Caboussat, J. W. He, A. V. Martynenko, C. Landry, C. Tong, and J. Seinfeld. A new atmospheric aerosol phase equilibrium model (UHAERO): organic systems, Atmos. Chem. Phys., 7, pages 4675–4698, 2007.
  45. N. R. Amundson, A. Caboussat, J. W. He, A. V. Martynenko, C. Landry, C. Tong, and J. Seinfeld. A new atmospheric aerosol phase equilibrium model (UHAERO): organic systems, Atmos. Chem. Phys. Discuss., 7, pages 8709–8754, 2007.
  46. N.R. Amundson, A. Caboussat, J.W. He, A.V. Martynenko, and J.H. Seinfeld. A phase equilibrium model for atmospheric aerosols containing inorganic electrolytes and organic compounds (UHAERO), with application to dicarboxylic acids, J. Geophysical Research, 112, D24S13, 2007.
  47. N. R. Amundson, A. Caboussat, J.W. He, C. Landry and J. H. Seinfeld, A Dynamic Optimization Problem Related to Organic Aerosols, C. R. Acad. Sci., 344(8), pages 519–522, 2007.
  48. A. Caboussat and M. Picasso and J. Rappaz, Modeling and Simulation of Liquid-Gas Free Surface Flows, in Free and Moving Boundaries, Analysis Simulation and Control, Lecture Notes in Pure and Applied Mathematics, Volume 252. Chapman and Hall/CRC, 2007.
  49. A. Caboussat, R. Glowinski, and J. M. Sicilian, Computation of the Normal Vector to a Free Surface by a Finite Element – Finite Volume Mixed Method, C. R. Acad. Sci., 343, pages 431–436, 2006.
  50. N. R. Amundson, A. Caboussat, J.-W. He, A.V. Martynenko, V.B. Savarin, J.H. Seinfeld, K.-Y. Yoo, A new inorganic atmospheric aerosol phase equilibrium model (UHAERO), Atmos. Chem. Phys., 6, pages 975–992, 2006.
  51. N. R. Amundson, A. Caboussat, J. W. He, A.V. Martynenko, V.B. Savarin, J.H. Seinfeld, K.-Y. Yoo. A computationally efficient inorganic atmospheric aerosol phase equilibrium model (UHAERO), Atmos. Chem. Phys. Discuss., 5, 9291–9324, 2005.
  52. N. R. Amundson and A. Caboussat and J.-W. He and J. H. Seinfeld, A Primal-Dual Interior-Point Method for an Optimization Problem Related to the Modeling of Atmospheric Organic Aerosols, J. Optim., Theory and Appl., 130(3), 375–407, 2006.
  53. A. Caboussat, A Numerical Method for the Simulation of Free Surface Flows with Surface Tension, Computers and Fluids, 35(10), pages 1205–1216, 2006.
  54. N. R. Amundson and A. Caboussat and J.-W. He and J. Seinfeld and K.-Y. Yoo, A Primal-Dual Active Set Algorithm for Chemical Equilibrium Problems Related to Modeling of Atmospheric Inorganic Aerosols, J. Optim., Theory and Appl., 128(3), 469–498, 2006.
  55. A. Caboussat and R. Glowinski, A Two-Grids/Projection Algorithm for Obstacle Problems, Computers and Mathematics with Applications, 50, pages 171-178, 2005.
  56. A. Caboussat and J. Rappaz, Analysis of a One-Dimensional Free Surface Flow Problem, Numer. Math., 101(1), pages 67–86, 2005.
  57. A. Caboussat, Numerical Simulation of Two-Phase Free Surface Flows, Archives of Computational Methods in Engineering, 12(2), pages 165–210, 2005.
  58. N. R. Amundson and A. Caboussat and J.-W. He and J. Seinfeld, An Optimization Problem related to the Modeling of Atmospheric Organic Aerosols, C. R. Acad. Sci., 340(10), pages 765–768, 2005.
  59. N. R. Amundson and A. Caboussat and J.-W. He and J. Seinfeld and K.-Y. Yoo, An Optimization Problem related to the Modeling of Atmospheric Inorganic Aerosols, C. R. Acad. Sci., 340(9), pages 683–686, 2005.
  60. A. Caboussat, R. Glowinski. On the Use of a Two-Grids Method in the Numerical Simulation of Free Boundary Problems, Proceedings LACSI symposium, Santa Fe, NM, October 2004.
  61. A. Caboussat and M. Picasso and J. Rappaz, Numerical Simulation of Free Surface Incompressible Liquid Flows Surrounded by Compressible Gas, J. Comput. Phys., 203(2), pages 626–649, 2005.
  62. A. Caboussat and V. Maronnier and M. Picasso and J. Rappaz, Numerical Simulation of Three Dimensional Free Surface Flows with Bubbles, Lecture Notes in Computational Science and Engineering, Springer-Verlag series, 35, pages 69–86, 2003.

PhD Thesis

  1. A. Caboussat, Analysis and Numerical Simulation of Free Surface Flows, PhD Thesis number 2893, Ecole Polytechnique Fédérale de Lausanne, December 2003. [link]