Bender, J., Izgin, T., Offner, Ph. and Torlo, D. (2025), The Lax–Wendroff theorem for Patankar-type methods applied to hyperbolic conservation laws. ArXiv preprint:2505.08387. PDF arXiv
CV
Education
- Ph.D. in Applied Mathematics, University of Zurich, 2020. Dissertation
- M.S. in Mathematics, University of Trieste and SISSA, 2016. Master Thesis
- B.S. in Mathematics, University of Milan–Bicocca, 2014.
- Diploma Liceo Scientifico Mascheroni, Bergamo, 2011.
Work experience
- 3/24–now: Assistant Professor (Ricercatore in Tenure Track)
- Università di Roma La Sapienza at Mathematics Department Guido Castelnuovo
- 12/21–3/24: SISSA Postdoctoral Fellow
- SISSA: International School of Advanced Studies - Trieste, Italy
- Project: Model order reduction techniques for advection dominated problems
- Group of prof. Gianluigi Rozza
- 10/20–11/21: Postdoctoral Fellow
- INRIA Bordeaux - Team CARDAMOM
- Projects: Stability of high order FEM with stabilization for advection problems, MOR for dispersive waves, exact solution of SW equations, high order methods for kinetic models for SW, high order entropy preserving/dissipative schemes
- Supervisor: prof. Mario Ricchiuto
- 09/16–08/20: Research and Teaching Assistant
- University of Zurich - Institute of Mathematics
- Teaching at Bachelor, Master and PhD students in Mathematics and Computer Science
- Supervisor: prof. Rémi Abgrall
- 09/10–08/16: Private Teacher
- Mathematics and Physics classes for high school and university students
- 01/10–06/16: Theatrical technician
- TACT International Act Festival Trieste
- Teatro Stabile Sloveno, Trieste
- Auditorium via Alberico da Rosciate, Bergamo
- Teatro Qoelet, Bergamo
- 01/10–06/14: Video editor
Main Collaborators
More Collaborators
- Walter Boscheri
- Mirco Ciallella
- Maria Han Veiga
- Lorenzo Micalizzi
- Monica Nonino
- Ivan Prusak
Co-tutoring
- Louis Petri (University of Mainz Master student)
- Ivan Prusak (SISSA PhD student)
- Gaia Buccino (Polimi Master student)
- Lorenzo Micalizzi (UZH PhD student)
- Mirco Ciallella (INRIA PhD student)
- Sixtine Michel (INRIA PhD student)
Skills
- Programming
- python
- Matlab
- Fortran
- Julia
- Languages
- Italian (Native)
- English (C1)
- German (B2)
- French (A1)
Reviewer
- Reviewer of Scientific Journals
Publications
- The Lax–Wendroff theorem for Patankar-type methods applied to hyperbolic conservation laws
- Friedrichs’ systems discretized with the Discontinuous Galerkin method: domain decomposable model order reduction and Graph Neural Networks approximating vanishing viscosity solutions
F. Romor, D. Torlo and G. Rozza. "Friedrichs' systems discretized with the DGM: domain decomposable model order reduction and Graph Neural Networks approximating vanishing viscosity solutions. (2025) " Journal of Computational Physics, 531, p. 113915. PDF DOI
- Structure preserving nodal continuous Finite Elements via Global Flux quadrature
Barsukow, W., Ricchiuto, M. and Torlo, D. (2025), Structure Preserving Nodal Continuous Finite Elements via Global Flux Quadrature. Numer Methods Partial Differential Eq., 41: e23167. https://doi.org/10.1002/num.23167. PDF DOI
- A time-adaptive algorithm for pressure dominated flows: a heuristic estimator
Prusak, I., Torlo, D., Nonino, M., Rozza, G. (2025). A Time-Adaptive Algorithm for Pressure Dominated Flows: A Heuristic Estimator. In: Marmo, F., Cuomo, S., Cutolo, A. (eds) Computational Mechanics and Applied Mathematics: Perspectives from Young Scholars. GIMC SIMAI Young 2024. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-76591-9_24 PDF DOI
- Analysis for Implicit and Implicit-Explicit ADER and DeC Methods for Ordinary Differential Equations, Advection-Diffusion and Advection-Dispersion Equations
Öffner, P., Petri, L., and Torlo, D. (2025). Analysis for Implicit and Implicit-Explicit ADER and DeC Methods for Ordinary Differential Equations, Advection-Diffusion and Advection-Dispersion Equations. Applied Numerical Mathematics, 212, p. 110-134. PDF DOI
- Calibration-Based ALE Model Order Reduction for Hyperbolic Problems with Self-Similar Travelling Discontinuities
Nonino, M., Torlo, D. Calibration-Based ALE Model Order Reduction for Hyperbolic Problems with Self-Similar Travelling Discontinuities. J Sci Comput 101, 60 (2024). https://doi.org/10.1007/s10915-024-02694-z PDF DOI
- A high-order, fully well-balanced, unconditionally positivity-preserving finite volume framework for flood simulations
M. Ciallella, L. Micalizzi, V. Michel-Dansac, P. Offner and D. Torlo. "A high-order, fully well-balanced, unconditionally positivity-preserving finite volume framework for flood simulations." Int J Geomath 16, 6 (2025). https://doi.org/10.1007/s13137-025-00262-7. PDF DOI
- Optimisation–Based Coupling of Finite Element Model and Reduced Order Model for Computational Fluid Dynamics
Prusak, I., Torlo, D., Nonino, M., Rozza, G. (2025). Optimisation–Based Coupling of Finite Element Model and Reduced Order Model for Computational Fluid Dynamics. In: Sequeira, A., Silvestre, A., Valtchev, S.S., Janela, J. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2. ENUMATH 2023. Lecture Notes in Computational Science and Engineering, vol 154. Springer, Cham. https://doi.org/10.1007/978-3-031-86169-7_28. PDF DOI
- Computations for Sustainability
Salavatidezfouli, S., Nikishova, A., Torlo, D., Teruzzi, M., Rozza, G. (2024). Computations for Sustainability. In: Fantoni, S., Casagli, N., Solidoro, C., Cobal, M. (eds) Quantitative Sustainability. Springer, Cham. https://doi.org/10.1007/978-3-031-39311-2_7 PDF DOI
- An optimisation-based domain-decomposition reduced order model for parameter-dependent non-stationary fluid dynamics problems
I. Prusak, D. Torlo, M. Nonino and G. Rozza. "An optimisation-based domain-decomposition reduced order model for parameter-dependent non-stationary fluid dynamics problems." (2024) Computers & Mathematics with Applications, 166, 253-268. PDF DOI
- On improving the efficiency of ADER methods
M. Han Veiga, L. Micalizzi and D. Torlo. "On improving the efficiency of ADER methods." Applied Mathematics and Computation, 466, page 128426, 2024. PDF DOI
- Efficient iterative arbitrary high order methods: an adaptive bridge between low and high order
L. Micalizzi, D. Torlo and W. Boscheri. "Efficient iterative arbitrary high order methods: an adaptive bridge between low and high order." Commun. Appl. Math. Comput. (2023). PDF DOI
- An optimisation-based domain-decomposition reduced order model for the incompressible Navier-Stokes equations
I. Prusak, M. Nonino, D. Torlo, F. Ballarin and G. Rozza. "An optimisation-based domain-decomposition reduced order model for the incompressible Navier-Stokes equations." Computers & Mathematics with Applications, 151 (2023) 172-189. PDF DOI
- A necessary condition for non oscillatory and positivity preserving time-integration schemes
T. Izgin, P. Öffner and D. Torlo. "A necessary condition for non oscillatory and positivity preserving time-integration schemes." (2024) In: Parés, C., Castro, M.J., Morales de Luna, T., Muñoz-Ruiz, M.L. (eds) Hyperbolic Problems: Theory, Numerics, Applications. Volume II. HYP 2022. SEMA SIMAI Springer Series, vol 35. Springer, Cham. https://doi.org/10.1007/978-3-031-55264-9_11. PDF DOI
- A new efficient explicit Deferred Correction framework: analysis and applications to hyperbolic PDEs and adaptivity
L. Micalizzi and D. Torlo. "A new efficient explicit Deferred Correction framework: analysis and applications to hyperbolic PDEs and adaptivity. " Commun. Appl. Math. Comput. (2023). https://doi.org/10.1007/s42967-023-00294-6. PDF DOI
- Weighted Reduced Order Methods for Uncertainty Quantification
Davide Torlo, Maria Strazzullo, Francesco Ballarin, and Gianluigi Rozza. Weighted reduced order methods for uncertainty quantification. In Francesco Ballarin Gianluigi Rozza, Giovanni Stabile, editor, Advanced Reduced Order Methods and Applications in Computational Fluid Dynamics, chapter 12, pages 251-264. Society for Industrial & Applied Mathematics, U.S., 2022. https://doi.org/10.1137/1.9781611977257.ch12 PDF DOI
- Spectral analysis of continuous FEM for hyperbolic PDEs: influence of approximation, stabilization, and time-stepping
Michel, S., Torlo, D., Ricchiuto, M. and Abgrall, R.. Spectral analysis of high order continuous FEM for hyperbolic PDEs on triangular meshes: influence of approximation, stabilization, and time-stepping. J Sci Comput 94, 49 (2023). PDF DOI
- High order entropy preserving ADER-DG scheme
E. Gaburro, P. Öffner, M. Ricchiuto and D. Torlo. "High order entropy preserving ADER-DG scheme." Applied Mathematics and Computation, 440:127644, 2023. doi:10.1016/j.amc.2022.127644. PDF DOI
- Arbitrary High Order WENO Finite Volume Scheme with Flux Globalization for Moving Equilibria Preservation
M. Ciallella, D. Torlo and M. Ricchiuto. (2022). "Arbitrary High Order WENO Finite Volume Scheme with Flux Globalization for Moving Equilibria Preservation. " Journal of Scientific Computing 96, 53 (2023). https://doi.org/10.1007/s10915-023-02280-9. PDF DOI
- Some preliminary results on a high order asymptotic preserving computationally explicit kinetic scheme
R. Abgrall and D. Torlo. (2022). "Some preliminary results on a high order asymptotic preserving computationally explicit kinetic scheme. " Communications in Mathematical Sciences, 20, 2, 297-326. https://dx.doi.org/10.4310/CMS.2022.v20.n2.a1. PDF DOI
- Model order reduction strategies for weakly dispersive waves
D. Torlo and M. Ricchiuto. "Model order reduction strategies for weakly dispersive waves. " Mathematics and Computers in Simulation, (205), pages 997-1028, 2023. PDF DOI
- An Arbitrary High Order and Positivity Preserving Method for the Shallow Water Equations
M. Ciallella, L. Micalizzi, P. Öffner and D. Torlo. (2022). "An Arbitrary High Order and Positivity Preserving Method for the Shallow Water Equations. " Computers & Fluids, 247, page 105630. PDF DOI
- Analytical traveling vortex solutions of hyperbolic equations for validating very high order schemes
M. Ricchiuto and D. Torlo. (2021). "Analytical traveling vortex solutions of hyperbolic equations for validating very high order schemes. " arXiv preprint, https://arxiv.org/abs/2109.10183. PDF arXiv
- Issues with Positivity-Preserving Patankar-type Schemes
D. Torlo, P. Öffner and H. Ranocha. (2022). "Issues with Positivity-Preserving Patankar-type Schemes. " Applied Numerical Mathematics, 182, 117-147. PDF DOI
- Relaxation Deferred Correction Methods and their Applications to Residual Distribution Schemes
R. Abgrall, E. Le Mélédo, P. Öffner and D. Torlo. (2022). "Relaxation Deferred Correction Methods and their Applications to Residual Distribution Schemes. " The SMAI Journal of computational mathematics, Volume 8 (2022), pp. 125-160. doi:10.5802/smai-jcm.82 PDF DOI
- Spectral analysis of continuous FEM for hyperbolic PDEs: influence of approximation, stabilization, and time-stepping
Michel, S., Torlo, D., Ricchiuto, M. and Abgrall, R.. Spectral Analysis of Continuous FEM for Hyperbolic PDEs: Influence of Approximation, Stabilization, and Time-Stepping. J Sci Comput 89, 31 (2021). https://doi.org/10.1007/s10915-021-01632-7 PDF DOI
- DeC and ADER: Similarities, Differences and a Unified Framework
M. H. Veiga, P. Öffner, and D. Torlo. (2021). "DeC and ADER: Similarities, Differences and a Unified Framework." Journal of Scientific Computing, 87, 2 (2021). https://doi.org/10.1007/s10915-020-01397-5. PDF DOI
- Arbitrary high-order, conservative and positivity preserving Patankar-type deferred correction schemes
P. Öffner and D. Torlo. (2020). "Arbitrary high-order, conservative and positivity preserving Patankar--type deferred correction schemes." Applied Numerical Mathematics, 153:15 – 34. PDF DOI
- High Order Asymptotic Preserving Deferred Correction Implicit-Explicit Schemes for Kinetic Models
R. Abgrall, and D. Torlo. (2020). "High Order Asymptotic Preserving Deferred Correction Implicit-Explicit Schemes for Kinetic Models." SIAM Journal on Scientific Computing, 42(3): B816--B845. PDF DOI
- Model Reduction for Advection Dominated Hyperbolic Problems in an ALE Framework: Offline and Online Phases
Torlo, D. (2025). Model Reduction for Advection Dominated Hyperbolic Problems in an ALE Framework: Offline, Online Phases and Error Estimator. In: Sequeira, A., Silvestre, A., Valtchev, S.S., Janela, J. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2. ENUMATH 2023. Lecture Notes in Computational Science and Engineering, vol 154. Springer, Cham. https://doi.org/10.1007/978-3-031-86169-7_42 PDF DOI
- Model order reduction for parametrized nonlinear hyperbolic problems as an application to uncertainty quantification
R. Crisovan, D. Torlo, R. Abgrall, and S. Tokareva. (2019). "Model order reduction for parametrized nonlinear hyperbolic problems as an application to uncertainty quantification." Journal of Computational and Applied Mathematics, 348:466 – 489. PDF DOI
- Weighted reduced order methods for parametrized partial differential equations with random inputs
Venturi, L., Torlo, D., Ballarin, F., Rozza, G. (2019). " Weighted Reduced Order Methods for Parametrized Partial Differential Equations with Random Inputs. " In: Canavero, F. (eds) Uncertainty Modeling for Engineering Applications. PoliTO Springer Series. Springer, Cham. https://doi.org/10.1007/978-3-030-04870-9_2 PDF DOI
- Stabilized weighted reduced basis methods for parametrized advection dominated problems with random inputs
D. Torlo, F. Ballarin, and G. Rozza. (2018). "Stabilized weighted reduced basis methods for parametrized advection dominated problems with random inputs." SIAM/ASA Journal on Uncertainty Quantification, 6(4): 1475--1502. PDF DOI
Service and leadership
- 10/22–10/24: Member of SISSA Senate
- 12/14–08/16: Faculty Students’ Representative
- 01/13–06/16: Organizer of Bergamo Beatles Festival
- 10/10–06/11: High School Students’ Representative
- 10/10–09/14: Active member of Associazione Giovanile Mellow Mood