- Boundary Integral Methods for Fractal Geometries, in collaboration with Prof. Maria Rosaria Lancia, La Sapienza University of Rome
In the framework of heat propagation, a Venttsel’ problem models the heat flow across highly conductive thin boundaries, which turns out to have several applications in physical and industrial processes (e.g. hydraulic fracturing, electrochemistry etc). We will reformulate this problem using a boundary integral approach for non-smooth surfaces and develop a suitable numerical method to study the problem numerically.
- Drop Electrohydrodynamics, in collaboration with Prof. Petia Vlahovska, Northwestern University
The idea is to bring together theoretical, numerical and experimental results to better understand the effect of electric fields on surfactant-covered drops.
- Error estimates for the evaluation of nearly singular integrals, in collaboration with Dr. Ludvig af Klinteberg and Prof. Anna-Karin Tornberg (KTH, Royal Institute of Technology)
The idea is to develop 3D error estimates for boundary integral methods where it is often necessary to evaluate layer potentials on or close to the boundary and where the underlying integral may be difficult to evaluate numerically and for which specialized quadrature techniques must be employed.
- The Arakawa scheme reinvented using the splitting technique and SBP operators: During May and November 2014, I was a guest of Jan Nordström, Professor in Scientific Computing and Head of Division of Computational Mathematics in the Department of Mathematics at Linköping University, Sweden. The Professor, another PhD student, Cristina La Cognata and I worked together to develop a finite difference discretization of the Jacobian operator in a mimetic way using SBP operator and compared this general formulation with the original formulation of Arakawa.
- The meteorological forecast operative at ARPA-Lazio: model results and comparison against measurements from the ARPA micrometeorological network: In 2011 I worked at CNR ISAC Institute of Tor Vergata together with Michele Spada, Ilaria Pietroni, Andrea Bolignano, Igor Petenko, Matteo Morelli, Roberto Sozzi and Stefania Argentini on the project The meteorological forecast operative at ARPA-Lazio: model results and comparison against measurements from the ARPA micrometeorological network presented at 32 nd NATO/SPS International Technical Meeting on Air Pollution Modelling and its Application, ITM 2012, May 7 – 11, Utrecht, The Netherlands.