Research
My research interests combine the development and analysis of mathematical models and of the ensuing numerical methods for the simulation of natural phenomena. I consider my work to be at the interface between applied mathematics and applications, and my personal aspiration is to contribute with my expertise to the solution of problems with social and environmental impacts.
Numerical methods for PDEs on surfaces
Development of numerical methods adapted to the geometry for scalar-, vector- and tensor-valued PDEs on surfaces (intrinsic finite volumes, Discontinuous Galerkin, surface finite element, high-order virtual element methods), on both stationary and evolving surfaces.
Main collaborators: M.W. Farthing, G. Manzini, S. Praetorius, M. Putti, A. Reusken, G. Scovazzi, A. Voigt
Related projects: FOR3013: Vector and Tensor Valued Surface PDEs (DFG, PI A. Voigt), UniPD-SID-2016 - Approximation and discretization of PDEs on Manifolds for Environmental Modeling (PI M. Putti)
Related publications:
- Convergence analysis of the intrinsic surface finite element method (submitted, 2025)
- Diffusion of tangential tensor fields: numerical issues and influence of geometric properties (J. Numer. Math., 2024)
- Arbitrary-order intrinsic virtual element method for elliptic equations on surfaces (Calcolo, 2021)
- Intrinsic finite element method for advection-diffusion-reaction equations on surfaces (J. Comp. Phys., 2021)
From surface geometry to physical response
Modeling, simulation, and inverse design: two-phase fluid deformable surfaces and multicomponent lipid vesicles, studying the interplay between surface geometry, phase coarsening and hydrodynamics; direct and inverse problems for transport on surfaces.
Main collaborators: D. Grazioli, V. Krause, A. Larese, I. Nitschke, A. Simone, A. Voigt
Related projects: BLUE-HEAT: The Geometric Blueprint of Thermal Transport for Energy Innovation (PI E. Bachini), FOR3013: Vector and Tensor Valued Surface PDEs (DFG, PI A. Voigt)
Related publications:
- Diffusion of tangential tensor fields: numerical issues and influence of geometric properties (J. Numer. Math., 2024)
- Derivation and simulation of a two-phase fluid deformable surface model (J. Fluid Mech., 2023)
- The interplay of geometry and coarsening in multicomponent lipid vesicles under the influence of hydrodynamics (Phys. Fluids, 2023)
Intrinsic Shallow Water Equations
Modeling and development of numerical methods to solve the Intrinsic Shallow Water Equations (ISWE) on fixed and moving surfaces: finite volumes with Eulerian and Lagrangian-Eulerian approaches, discontinuous Galerkin schemes, continuous Galerkin with entropy-viscosity stabilization, including wetting-and-drying transitions and variable topography.
Main collaborators: E. Abreu, C. Dawson, M.W. Farthing, R. Nomura, J. Perez, M. Putti
Related projects: MONUGEO - Modern numerical methods for high-fidelity simulation of geohazards (HORIZON-MSCA-2023-SE-01), RETURN - multi-Risk sciEnce for resilienT commUnities undeR a changiNg climate (PNRR, Next-Generation EU)
Related publications:
- A robust Lagrangian-Eulerian Finite Volume scheme for intrinsic shallow water equations with wetting-and-drying transitions on locally discontinuous beds (submitted, 2026)
- A geometrically intrinsic Lagrangian-Eulerian scheme for 2D shallow water equations with variable topography and discontinuous data (Appl. Math. Comput., 2023)
- Intrinsic finite element method for advection-diffusion-reaction equations on surfaces (J. Comp. Phys., 2021)
- Geometrically intrinsic modeling of shallow water flows (ESAIM M2AN, 2020)
Coupled models & hydrological networks
Formulation and numerical solution of geometrically intrinsic models for coupled surface-subsurface hydrological applications; modeling of flow and transport in porous media with strong anisotropy; dynamics of river networks.
Main collaborators: G. Botter, M. Camporese, N. Durighetto, M. Ghinassi, A. Larese, M. Putti
Related projects: Metodi numerici integrati per la simulazione e la prevenzione del dissesto idrogeologico (INdAM-GNCS 2026), RETURN - multi-Risk sciEnce for resilienT commUnities undeR a changiNg climate (PNRR, Next-Generation EU), HYDROSEM - Fluvial and tidal meanders of the Venetian-Po plain (CARIPARO, PI M. Ghinassi)
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