BOTTI Lorenzo Alessio

Overview of research activity.
Partial Differential Equations (PDEs) are widely employed to model physical problems in engineering based on the continuum mechanics and continuum thermodynamics approach. In this context, numerical strategies for the approximate solution of PDEs are carefully designed and validated, in particular, the theoretical results of a-priori convergence analyses can be verified by testing numerical implementations against analytical or manufactured solutions. High-order schemes might achieve satisfactory error reduction (with respect to the exact solution) by enriching the functional representation of the numerical solution, specifically, the convergence rates can be predicted in each region of the computational domain according to the local solution regularity. Besides the aforementioned error reduction capabilities, the efficiency of computational modelling tools is subdued to the availability of effective solution strategies for the large scale sparse equation systems arising from spatial and temporal discretizations, a-posteriori error analysis tools for driving adaptive solution enrichment strategies and effective High Performance Computing (HPC) implementations of the algorithms on parallel architectures. My research activity deals with development, implementation and validation of numerical methods and solution strategies for numerical methods in the field of fluid mechanics and contact mechanics.
Shortlist of Research Topics.
-High-order accurate nonconforming formulations for the numerical solution of PDEs: Discontinuous Galerkin (DG), Hybridizable Discontinuous Galerkin (HDG) and Hybrid High-Order
methods (HHO).
-Computational continuum mechanics: Computational Fluid Dynamics (CFD), turbulence modeling (DNS, ILES, RANS) and Computational Contact Mechanics (CCM).
-Efficient multilevel solution strategies for DG, HDG and HHO discretizations.
-High-order accurate discretications on non-polyhedral meshes (with mesh elements featuring
curved boundaries) and on very general polytopal elements meshes.
-Distributed and shared memory parallelism on multi- and many-cores architectures.
-Development of scientific computing libraries providing computational modeling tools for implementing nonconforming formulations on general meshes.
-Applications: Hemodynamics, aerodynamics, aeronautics, turbomachinery, flow in porous media, poroelasticity, finite deformations of hyperelastic materials (blow molding), multicomponent incompressible flows (drop collisions on liquid)