Zurich Colloquium in Applied and Computational Mathematics

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Speaker

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12 March 2025
16:00-17:00

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

Abstract

Turbulent mixing induced by hydrodynamic instabilities occurs when two fluids of different densities, velocities, and viscosities interact. Theoretical, experimental, and numerical efforts to understand and predict the dynamics of hydrodynamic instabilities are very important for science and engineering applications. Statistical convergence and turbulence quantification are crucial for achieving reliable and accurate modeling and simulations. In this talk, we present an increasingly accurate and robust front-tracking/ghost-fluid method with higher-order weighted essentially non-oscillatory schemes used for the numerical simulations of Rayleigh-Taylor and Richtmyer-Meshkov Instabilities. We investigate the time evolution of velocity fields and fluctuations for different configurations to explore the scaling law of the energy spectrum.

Statistical convergence of turbulence

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

Event Details