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 (systems of) parametrized partial differential equations in the manyquery or realtime context thanks to offlineonline computational splittings, such as (shape) optimization, flow control, characterization, parameter estimation, uncertainty quantification. Our research is mostly based, but not limited to, 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.
 FLUIDSTRUCTURE 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
 OPEN SOURCE SOFWARE DEVELOPMENT Several open source software libraries are developed and maintained
Research Group

Antonio De Simone, Professor

Gianluigi Rozza, Professor

Andrea Cangiani, Associate Professor

Luca Heltai, Associate Professor

Giovanni Noselli, Associate Professor

Michele Girfoglio, Assistant Professor

Guillaume Bonnet, Research fellow

Laura Meneghetti, Research fellow

Davide Torlo, Research fellow

Giulio Ortali, PhD Student (in cotutela with TU/Eindhoven)

Marco Feder, PhD Student

Valentin Nkana Ngan, PhD Student

Moaad Khamlich, PhD Student
Visiting Professors

Andrea Mola, IMT Lucca

Giovanni Stabile, Visiting Professor
Main External Collaborators

Nirav Vasant Shah, PhD Student (in cotutela with Univ. of Santiago de Compostela)

Federico Pichi, Other

Francesco Ballarin, Università Cattolica, Brescia

Alfio Quarteroni, Politecnico di Milano

Peregrina Quintela, Full professor at University of Santiago de Compostela

François Alouges, CMAP (Ecole Polytechnique), Paris
Collaborating Institutes
 Politecnico di Milano, MOX, Modeling and Scientific Computing Center
 EPFL, Lausanne, Switzerland
 Massachusetts Institute of Technology, Cambridge, US
 Università di Pavia, Italy
 University of Houston, US
 University of Toronto, Canada
 Laboratoire Jacques Louis Lions, Paris VI, France
 Duke University, Durham, US
 Imperial College, London, UK
 Politecnico di Torino, Italy
 Virginia Tech, Blacksburg, Virginia, US
 Scuola Superiore S.Anna, Pisa, Italy
 University of Cambridge, UK
 University of Sevilla, Spain
 University of Santiago de Compostela, Spain
 RWTH Aachen, Germany
 University of Ghent, Belgium