Zurich Colloquium in Applied and Computational Mathematics

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26 February 2025
16:30-17:30

Prof. Dr. Philippe Ciarlet
Institut für Mathematik, Universität Zürich

Event Details

Speaker invited by

Prof. Dr. Stefan Sauter

Abstract

As is well-known, Koiter's model is often used in numerical simulations, because it is a two-dimensional model that captures well the "membrane-dominated" and "flexural-dominated" effects that arise in a nonlinearly elastic shell subjected to applied forces and specific boundary conditions. Finding a satisfactory existence theory for this nonlinear shell model has stood as an open problem for a very long time. The present work, which is a joint work with Cristinel Mardare, provides a two-dimensional model that preserves all the virtues of Koiter's model, while being in addition amenable to a satisfactory existence theory. More precisely, our new two-dimensional mathematical model for a nonlinearly elastic shell takes the form of a minimization problem with a stored energy function that is polyconvex and orientation-preserving, and more generally satisfies all the other assumptions of John Ball's existence theorem. In addition, the most noteworthy feature of this model is that it is "of Koiter's type", in the sense that for a specific class of deformations that are "to within the first order" identical to those introduced by W.T. Koiter for defining his model, the "lowest order part" of its stored energy function coincides with the stored energy function of Koiter's model.

A two-dimensional nonlinear shell model of Koiter's type

HG G 19.2

12 March 2025
16:30-17:30

Dr. Enrico Zampa
University of Vienna

Event Details

Speaker invited by

Prof. Dr. Ralf Hiptmair

Abstract

Incompressible magnetohydrodynamics (MHD) and the incompressible Godunov-Peshkov-Romenski (GPR) model share a similar structural framework, with key properties such as energy conservation, incompressibility, and involutions. In this talk, we demonstrate how to preserve these essential properties at the fully discrete level using compatible finite element methods, combined with a tailored time integration scheme. Furthermore, we explore both linear and nonlinear stabilization strategies necessary for convection-dominated regimes, examining their interplay with structure preservation. In particular, we show that such stabilizations affect only energy conservation. This research was conducted in collaboration with M. Dumbser from the University of Trento.

Structure-preserving discretization of incompressible magnetohydrodynamics and the incompressible Godunov-Peshkov-Romenski model

HG G 19.2

19 March 2025
16:30-17:30

Prof. Dr. Tulin Kaman
University of Arkansas, USA

Event Details

Speaker invited by	Prof. Dr. Ralf Hiptmair

Title T.B.A.

HG G 19.2

26 March 2025
16:30-17:30

Dr. Nicolas Boullé
Imperial College London

Event Details

Speaker invited by

Prof. Dr. Rima Alaifari

Abstract

There is a mystery at the heart of operator learning: how can one recover a non-self-adjoint operator from data without probing the adjoint? Current practical approaches suggest that one can accurately recover an operator while only using data generated by the forward action of the operator without access to the adjoint. However, naively, it seems essential to sample the action of the adjoint for learning time-dependent PDEs. In this talk, we will first explore connections with low-rank matrix recovery problems in numerical linear algebra. Then, we will show that one can approximate a family of non-self-adjoint infinite-dimensional compact operators via projection onto a Fourier basis without querying the adjoint.

Operator learning without the adjoint

HG G 19.2

2 April 2025
16:30-17:30

Prof. Dr. Pavel Exner
Nuclear Physics Institute of the CAS

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