Masterclass in Numerical Analysis and Scientific Computing
Abstract
Many physical problems involving heterogeneous spatial scales, such as the flow-through fractured porous media, the study of fiber-reinforced materials or the modeling of blood circulation in living tissues, just to mention a few examples, can be described as coupled partial differential equations defined in domains of heterogeneous dimensions that are embedded into each other.
The definition and the approximation of coupling operators that are suitable for this problem is still a challenge. I will present a general mathematical framework for the analysis and the approximation of partial differential equations coupled with non-matching constraints across different scales, focussing on their enforcement using the Lagrange multiplier. I will discuss in general terms the well-posedness, stability, robustness of the problem with respect to the small scale, and their numerical approximation.
Brief Biography
Bio:
Luca Heltai has been an Associate Professor in Numerical Analysis at the International School for Advanced Studies, in the Applied Mathematics Laboratory "mathLab" since 2012. He has been a research associate at Penn State College of Earth and Mineral Sciences, State College (USA) in the group of Prof. Francesco Costanzo in 2006 and 2007, and he obtained his Ph.D. in Mathematics and Scientific Computing at the University of Pavia, under the supervision of Prof. Daniele Boffi, in 2006.
Professor Heltai was a Fulbright scholar at the Courant Institute of Mathematical Sciences in New York (USA), and a visiting faculty at the Ecole Polytechnique de Paris, at the Universitat Politecnica de Catalunya, at the Weierstrass Institute for Applied Analysis and Stochastics, and at the King Abdullah University of Science and Technology.
Luca has been the director and co-founder of the joint SISSA-ICTP Master's program in High-Performance Computing (http://www.mhpc.it) from 2014 to 2022, and he contributed to the design and establishment of the Master’s Degree in Data Science and Scientific Computing offered jointly by SISSA, ICTP, University of Trieste, and University of Udine (http://www.dssc.units.it).
Professor Heltai is an expert in the development of numerical methods and algorithms for the solution of biological, physiological, and industrial problems modeled by partial differential equations, and he is one of the main developers of the open-source library deal.II (http://www.dealii.org) for the High-Performance computing solution of partial differential equations.