The research of 4 members of the group (details at https://sites.google.com/view/vembic) is largely carried out in the context of the development of the Virtual Element Method (VEM), a numerical methodology based on general polyhedral partitions for the discretization and solution of partial derivative problems. This area of research is supported by the ERC-SYG NEMESIS European fund (details at https://erc-nemesis.eu/) and by several PRIN funds (identification codes 20204LN5N5, PNRR-P2022BH5CB, 2022MBY5JM,202292JW3F). The research of the UniMiB numerics group is also combined in other important lines of research, involving, for example, the development and analysis of the finite element method (in many of its different declinations), the efficient and robust resolution of linear systems, the approximation of multivariate data and signal analysis.

Topics:

• VEM development for problems with complex geometries and in multi-physics
• Finite Elements for advanced fluids, such as in magnetohydrodynamics or non-Newtonian
• Virtual elements in solid/fluid mechanics and their use in the engineering world
• Construction and adaptation of two- and three-dimensional grids composed of generic polygons and polyhedra
• Space-time Galerkin methods
• Development and analysis of discontinuous Galerkin-type methods for kinetic equations
• Study of robust solvers (using multilevel and domain decomposition techniques) for a wide range of approximations and PDEs
• Spectral analysis and Krylov/multigrid methods for linear systems resulting from the approximation of differential/integral equations
• Multivariate approximation of sparse data using "kernel-based" methods and study of techniques to detect discontinuities in a discrete signal

Participants:

• Blanca Ayuso de Dios
• Lourenco Beirao da Veiga
• Franco Dassi
• Lorenzo Mascotto
• Milvia Francesca Rossini
• Alessandro Russo
• Cristina Tablino Possio