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Numerical Analysis and Scientific Computing

The research deals with the analysis, development, application of mathematical models for the integration of complex systems. The analysis is conducted using mathematical methods in several fields such as linear algebra, approximation theory, partial differential equations, optimization and control. Solution methods are developed and applied to domains as diverse as (potential and viscous) flow dynamics, (linear and nonlinear) structural analysis, mass transport, heat transfer and in general to multiscale and multiphysics applications. The methods have been integrated into complex multidisciplinary systems.

Research topics

  • CONTROL AND OPTIMIZATION
  • The efficient solution of optimal control or shape optimization problems involving partial differential equations (PDEs) is a problem of interest in computational science and engineering. The goal of an optimal control problem is the minimization/maximization of a given output of interest (expressed by suitable cost functionals) under some constraints, controlling either suitable variables (such as sources, model coefficients or boundary values) or the shape of the domain itself. In the latter case, we deal with shape optimization or optimal shape design problems.
  • REDUCED ORDER MODELLING
  • Model order reduction techniques provide an efficient, accurate and reliable way of solving parametrized partial differential equations in the many-query or real-time context, such as (shape) optimization, characterization, parameter estimation and control. Our research is based on certified reduced basis methods and proper orthogonal decomposition for parametrized PDEs.
  • FREE SURFACES
  • Techniques to study the position of an interface as a part of the problem itself, when studying the dynamics of a boat, for example.
  • FLUID-STRUCTURE INTERACTION
  • Development of efficient algorithms and methods for the coupling between the fluid and structure dynamics finds applications in a large variety of fields dealing with internal or external flows, also at the reduced order level (cardiovascular applications, naval engineering).
  • PARALLEL and HIGH PERFORMANCE COMPUTING

 

Research Group

Visiting Professors

 

Main External Collaborators

Collaborating Institutes

  • Politecnico di Milano, MOX, Modeling and Scientific Computing Center
  • EPFL, Lausanne, Switzerland
  • Massachusetts Institute of Technology, Cambridge, US
  • Universita' di Pavia
  • University of Houston

 

Grants

ERC CoG 2015 AROMA-CFD grant 681447: Advanced Reduced Order Methods with Applications in Computational Fluid Dynamics (PI Prof. Gianluigi Rozza)

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