Davide Torlo’s Personal Website

Hello visitor! I am Davide Torlo, a Postdoctoral Fellow at SISSA in prof. Rozza’s group. Previously researcher at INRIA Bordeaux in CARDAMOM team, under the supervision of prof. Mario Ricchiuto. I earned my PhD at University of Zurich under the supervision of prof. Rémi Abgrall. Before, I studied in SISSA and University of Trieste for my Master, where I did my thesis with prof. Gianluigi Rozza, and at University of Milan - Bicocca for my Bachelor studies.

Current research

Currently I have a SISSA Mathematical Fellowship and I work in prof. Rozza’s group on Model Order Reduction for advection dominated problems. I have also various Numerical Analysis projects on hyperbolic PDEs, structure preserving methods for ODEs and PDEs and arbitrarily high order methods.

  1. Reduced order models for advection dominated problems. These problems have a very slow decay of the Kolmogorov n-width. Hence, specific techniques must be used to obatain computational reduction. Ingredients that I retain fundamental in this topic are: an arbitrary-Lagrangian-Eulerian formulation, a geometrical calibration of the solutions, an optimization technique and a forecast of such calibration.
  2. Applications of the mPDeC to shallow water equations for very accurate and positivity preserving schemes. Check out Shallow Water mPDeC WENO Island simulation
  3. Reduced model for dispersive waves. The goal is to split dispersive waves equations into hyperbolic and elliptic part and to reduce the model for the elliptic part of the problem. Dispersive Waves
  4. Arbitarily high order time integration schemes. I am often working with the Deferred Correction (DeC) time integration method or with ADER. I study their properties and their possible extentions to structure preserving schemes. Check out ADER is DeC and mPDeC.
  5. Stabilized Finite Element methods. We are studying highly accurate space and time discretization for hyperbolic problems. We use different time integrators, space discretizations and stabilization techniques. The goal is to find the stability regions and the best perfomant scheme. Dispersion analysis
  6. Kinetic models with macroscopic Shallow Water equations limit. Also here the use of an implicit DeC scheme allows to obtain high order methods. Kinetic SW
  7. Issues with modified Patankar schemes, which are positive preserving schemes, but can show oscillations and inconsistency under certain conditions. Issues MP Robertson Problem MP

Previous Projects

During my previous contracts I’ve studied high order accurate methods and model order reduction techniques for hyperbolic problems. The dissertation of my PhD is available here.

  1. I have studied an implicit–explicit discretization for kinetic models with arbitrary high order accuracy, through the Deferred Correction as time integration scheme and Residual distribution for the spatial discretization. Publication on the topic Shu Osher test
  2. MOR techniques for hyperbolic problems for advection dominated problems with an ad hoc arbitrary Lagrangian–Eulerian model to track the steep fronts, here, and for uncertainty quantification applications here.

EulerianLagrangian

  1. Weighted MOR algorithm to speed up the computation in stochastic PDE. I wrote a post on that and there is a publication about it. Advection Dominated