Calculus of Variations and Geometric Measure Theory

The interplay of geometric modelling and numerical analysis of PDEs

created by braidesa on 15 Jan 2019

24 jan 2019 - 25 jan 2019   [open in google calendar]

Dipartimento di Matematica - Università di Roma "Tor Vergata"

Abstract Over the last fifty years, computer simulations have dramatically increased their impact on research, design and production, and are now an indispensable tool for development and innovation in science and technology. Partial Differential Equations (PDEs) offer a broad and flexible framework for modelling and analysing a number of phenomena arising in fields as diverse as physics, engineering, biology, and medicine. Not surprisingly, research on methods to simulate PDEs have a central role in modern science. In reality, the simulation of PDEs is a brick within a workflow where, at the beginning, the geometrical entities are created, described and manipulated with a geometry processor, often through Computer-Aided Design systems (CAD), and then used as input in Computer-Aided Engineering systems (CAE) where they are handled and processed for the simulation. The representation of geometric entities has its roots in geometric modelling, and often the requirements of shape design are different from those of simulation, which is based on numerical methods for PDEs. The simulation of PDEs on CAD geometries (which are mainly represented through their boundaries) calls then for (re-)meshing and re-interpolation techniques that are computationally expensive and result in non-exact geometries as well as inaccurate solutions. In this course, A. Buffa will give an introduction to the recent scientific efforts devoted to tackle this bottleneck both from the perspective of geometric modelling and of the numerical analysis of PDEs. From volumetric modelling to the framework of isogeometric analysis, within a mathematical perspective, she will provide an overview of the state of the art and of the many questions that are still open.

Annalisa Buffa is professor of Numerical Modelling and Simulation at the Mathematical Institute of Computational Science and Engineering of the École Polythechnique Fédérale de Lausanne; she is the PI of the ERC Advanced Grant 2016-2021 CHANGE "New CHallenges for (adaptive) PDE solvers: the interplay of ANalysis and GEometry". Among the many invitations and awards, we recall the invitation to the ICM 2014 as speaker in the Numerical Analysis and Scientific Computing section, the ICIAM Collatz Prize 2015, and the election as a corresponding member of the Accademia dei LIncei in 2018. She is the Jacques-Louis Lions Lecturer 2018.

This course is part of the MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata, CUP E83C18000100006

Organizers: Andrea Braides, Carla Manni.

Speakers: Annalisa Buffa.