Numerics on Hamilton Jacobi equations

An efficient algorithm for Hamilton-Jacobi equations in high dimension, (with M. Falcone, R. Ferretti), Computing and Visualization in Science, Vol.7,No.1,(2004), 15-29.

A weighted essentialy non oscillatory, large time-step scheme for Hamilton Jacobi equations, (with R.Ferretti, G.Russo). SIAM J. Sci. Comp., 27 (3) (2005), 1071--1091.

Convergence for first order scheme for non-local eikonal equation, (with O.Alvarez, R.Monneau, E.Rouy). IMACS J. Appl. Numer. Math. 56(9) (2006), 1136-1146.

Convergence of a Generalized Fast Marching Method with sign changing velocity for an eikonal equation, (with M. Falcone, N. Forcadel, R. Monneau). SIAM J. Numer. Anal. 46 (2008), 2920-2952.

Application of Optimal Control techniques and Advanced Computing to the study of enzyme kinetics, (with  P. Lanucara, M. Rorro, V. Ruggiero)  Mathematics and Computers in Simulations. 81 (3), (2010) pp. 705-716.

A Generalized Fast Marching Method on Unstructured Triangular Meshes (with M. Falcone, P. Hoch), SIAM J. Numer. Anal., 51 (2013), pp. 2999-3035.

A flame propagation model on a network with application to a blocking problem, (with F. Camilli, C.Marchi),(2015), arXiv:1411.3260

Numerics on Dislocation Dynamics

Dislocation Dynamics described by non-local Hamilton-Jacobi equations (with O.Alvarez, Y. Le Bouar, P.Hoch, R.Monneau), Materials Science and Engineering A-structural Materials Properties Microstuctures and Processing,  400-4001 (2005), 162-165.

A convergent scheme for a non local Hamilton-Jacobi equation modelling dislocation dynamic,(with O.Alvarez, R.Monneau, E.Rouy). Numerische Mathematik 104 (4) (2006), 413-444.

A non-monotone Fast Marching scheme for a Hamilton- Jacobi equation modelling dislocation dynamics, (with E.Cristiani, N.Forcadel), Numerical Mathematics Advanced Applications- ENUMATH2005, Springer, Berlino(2006),  724-731.

A Generalized Fast Marching Method for dislocation dynamics, (with N. Forcadel, R. Monneau), SIAM J.Numer. Anal., 49 (2011), pp. 2470-2500.

Numerics on  Mean Curvature Motion

A time adaptive semi Lagrangian approximation to Mean Curvature Motion, (with M. Falcone, R. Ferretti). Numerical Mathematics Advanced Applications- ENUMATH2005, Springer, Berlino(2006), 732-739.

A Semi-Lagrangian scheme for the curve shortening flow in codimension 2 , (with M. Falcone, R. Ferretti). Journal of Computational Physics, 225, No. 2 (2007), 1388-1408.

A single-pass scheme for the Mean Curvature Motion of convex curve, Numerical Mathematics and Advanced Applications-ENUMATH2007, Springer, Heidelberg (2008), 671-678.

A Semi-Lagrangian approximation of min-max type for the stationary mean curvature equation,       (with R. Ferretti). Numerical Mathematics and Advanced Applications-ENUMATH2007, Springer, Heidelberg (2008),  679-686.

Image Processing

Convergence of a large time–step scheme for Mean Curvature Motion, (with M.Falcone, R. Ferretti) Interfaces and Free Boundaries, 12 (4), (2010), pp. 409-441.

A Semi-Lagrangian approximation for the AMSS model of image processing, (with R. Ferretti) Applied Numerical Mathematics, 73 (2013), pp. 16-32.

A Semi-Lagrangian scheme for Area Preserving Flows, (with R. Ferretti) Proceedings IEEE International Conference on Pattern Recognition,(2012), pp. 2029-2033.

A brief survey on semi-Lagrangian schemes for Image Processing, (with M. Falcone, A. Festa),  “Mathematics for Visualization”,  Springer Series vol. 23, Heidelberg 2013, pp. 191-218.

A Semi-Lagrangian scheme with Radial Basis approximation for Surface reconstruction (with R.Ferretti),  R. Comput. Visual Sci. (2016). doi:10.1007/s00791-016-0274-2

Numerics on  Mean Field Games

A fully discrete Semi-Lagrangian scheme for a first order mean field games problem (with F.J. Silva), SIAM J. Numer. Anal. 52 (2014), pp. 45-67.

Semi-Lagrangian schemes for a mean field games problems (with F.J. Silva) In Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on, pp. 3115-3120.

A model problem for Mean Field Games on networks (with F. Camilli, C. Marchi),  "Optimal control problems and related fields", DCDS-A, Vol. 35, no.( 2015), pp. 4173-4192.

Semi-Lagrangian scheme for a degenerate second order Mean Field Game system (with F.J. Silva)  "Optimal control problems and related fields", DCDS-A ,  Vol. 35, no.( 2015), pp. 4269-4292 .

A Semi-Lagrangian scheme for a modified version of the Hughes model for pedestrian flow (with A. Festa, F. J. Silva, M-T. Wolfram) ``Dynamic Games and Applications’’ (2016),pp. 1-23 .

A Semi-Lagrangian scheme for the Fokker-Planck equation (with F.J. Silva) IFAC Proceeding of the conference CPDE’16 (2016), 49 (8), pp. 272-277.