History of Numerical Analysis

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Alfio Quarteroni

Oral History (pdf)                                                                     

Interviewer:Philip Davis

Professor Alfio Quarteroni discusses a range of topics in this interview with Phil Davis, including his work on finite elements, spectral methods, and domain decomposition. He began studying economic issues in a more professional school before switching over to study mathematics. Quarteroni received his Ph.D. from University of Pavia in Italy, completing a thesis on finite methods under Franco Brezzi. He finished it up in Paris, at the Laboratoire d'Analyse Numérique (now called the Laboratorie Jacques-Louis Lions), where he was encouraged to begin studying spectral methods. Professor Enrico Magenes, who dominated mathematics at Pavia, also exerted a strong influence on Quarteroni. Quarteroni observes how numerical methods have gone from obscure, rarely-used tools to common ones, although they are still not popular in some quarters of the engineering community. Quarteroni notes that low-order methods such as finite elements and higher-order methods such as spectral methods seem to be merging. Numerical methods are necessarily tied to experimental data. One of the challenges, especially in the airplane industry, is multi-objective optimization involving various fields of mathematics and physics. Quarteroni later became interested in domain decomposition, an area that became important with the rise of parallel computing but which are now important in a variety of fields, including the design of racing yachts. Quarteroni has been heavily involved in addressing various fluid dynamics problems central to the design of America's Cup boats, and his work recently helped boost the Swiss team to an unexpected victory. He enjoys teaching both engineering and math students, which he currently does both at the Politecnico di Milano in Italy and at the Polytechnic Institute of Lausanne in Switzerland. The former, Quarteroni notes, is the best technical institute in Italy and the latter is one of the most international educational institutions in all of Europe, attracting students from across Europe and the world. Quarteroni also discusses prominent figures in Italian mathematics, including Mauro Picone, for whom the Picone Institute is named, Gaetano Fichera, and Ennio De Giorgi.

Key words:  spectral methods,  finite element methods, domain decomposition, Navier-Stokes equation, multi-objective optimization, cardiovascular flow, America's Cup yacht (Alinghi)

Time frame: 1970's, 1980's, 1990's

People:  Franco Brezzi, Enrico Magenes, Roland Glowinski, Pierre-Arnaud Raviart, Claudio Canuto, Mauro Picone, Gaetano Fichera, Ennio De Giorgi

Location:  University of Pavia,  Politecnico di Milano, Ecole Polytechnique Fédérale de Lausanne

Citation:  Alfio Quarteroni, Oral history interview by Philip Davis, 22 June, 2004, Brown University. Society for Industrial and Applied Mathematics, Philadelphia, PA


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