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People with expertise in this area
Research interests

Giacomo Albi: Associate Professor
Marco Caliari: Full Professor

Elena Gaburro: Associate Professor

Research interests
Topic	People	Description
Exponential integrators and approximation of matrix functions	Marco Caliari	Analysis and implementation of exponential integrators for stiff equations by efficiently approximating matrix functions of exponential type, with application to systems of diffusion-reaction equations (Turing pattern), nonlinear Schrödinger equations, and Ginzburg-Landau equations (soliton and vortex dynamics).
Numerical methods and models for multi-scale systems of interacting particles	Giacomo Albi	Analysis and implementation of mathematical methods and models for dynamics of systems of interacting particles on various scales and their control: data-driven control for high-dimensional systems with non-local interaction; particle methods for problems of global optimization and applications to machine learning; dynamics of opinions on social networks; multi-scale models for crowd dynamics, and optimal strategies for evacuation problems; socio-epidemiological models and strategies to mitigate the spread of infection; control problems for high energy particles for the confinement in plasmas, and for targeted radiotherapy in treatment of tumors.
Numerical solution of partial differential equations	Giacomo Albi Marco Caliari Elena Gaburro	Analysis and implementation of innovative and effective numerical methods for solving and controlling partial differential equations (PDEs) of parabolic type (diffusion-transport-reaction), hyperbolic type (e.g. Euler equations for gas dynamics and Einstein field equations for astrophysics), highly oscillatory (Schrödinger equations), and integro-differential equations (kinetic equations with term collision and mean-field equations with non-local interaction terms).
Development of novel Finite Volumes and Galerkin Discontinuous numerical methods with Structure Preserving properties	Elena Gaburro	Conception, analysis and HPC development of novel high-order accurate Finite Volumes (FV) and Discontinuous Galerkin (DG) numerical methods for the solution of hyperbolic equations. The equations of interest are: the Euler equations of gas-dynamics, Shallow Water equations for the field of fluid-dynamics, MHD and GRMHD for magnetohydrodynamics, Baer-Nunziato for multiphase, GPR for continuum mechanics and the Einstein field equations for general relativity. The methods developed are high-order accurate, structure preserving (i.e., preserving additional physical features as equilibria, involution constraints and asymptotic limits) and Arbitrary-Lagrangian-Eulerian (ALE). The algorithms are implemented on adaptive Cartesian grids and on grids of triangles/tetrahedra, polygons/polyhedra and Voronoi also moving in time (the mesh generation and optimization are also the subject of our research).