Department of Mathematics

Time and Place: Tuesdays 3:05-4:20 pm in Room 0231, Love Building

Course: MAP 6939

Scope: The Applied and Computational Math Seminar is series of talks with various topics covering a broad spectrum of not only applied and computational mathematics but also engineering. Researchers outside of the Department of Mathematics and Florida State University, postdocs and senior Ph.D students are also welcomed to share their work. Please contact the organizer if you wish to schedule your talk. For Spring 2023, contact Kyle Gallivan (gallivan"at"math.fsu.edu)

Abstract: This presentation contains a short introduction to the basics of a popular reduced order modelling techniques for parametrized partial differential equations, namely reduced basis methods. For simplicity, the introduction will focus on the case of elliptic equations. Reduced basis methods are typically based on an offline/online paradigm. For what concerns the offline phase, we will discuss training of reduced basis spaces by means of the so-called greedy algorithm, or by means of proper orthogonal decomposition. The former requires the availability of an a posteriori error estimator, which expression will be discussed for the elliptic case. During the online phase, the reduced order model is evaluated by performing a Galerkin method on the generated reduced basis space. Practical assumptions on how to obtain a cheap online evaluation will be discussed. If time permits, the presentation will finish with an extension to a different class of problems, and a brief discussion of the author's ongoing research interests.

Bio: Dr. Francesco Ballarin is a researcher in applied mathematics, in the field of numerical analysis and mathematical modeling for systems governed by partial differential equations. He graduated in Mathematical Engineering at Politecnico di Milano, defending his BSc thesis in 2009 and MSc thesis in 2011. He then pursued a PhD in Mathematical Models and Methods in Engineering at MOX, Department of Mathematics, Politecnico di Milano, defending his PhD thesis in 2015 under the supervision of Prof. Alfio Quarteroni. After his PhD, he has been post-doctoral research fellow (2015-2018) and Assistant Professor in Numerical Analysis (2018-2021) at SISSA mathLab in the group of Prof. Gianluigi Rozza. Since March 2021, Francesco is a Tenure-track Assistant Professor in Numerical Analysis at the Department of Mathematics and Physics, Università Cattolica del Sacro Cuore, Brescia, Italy. His research focuses in particular on reduced order methods (ROMs) for parametrized problems in computational fluid dynamics. Such methods are required by several applications in engineering and life sciences in order to reduce the computational time for the simulation of complex problems.