Zurich Colloquium in Applied and Computational Mathematics

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24 April 2024
16:30-18:00

Prof. Dr. Guglielmo Scovazzi
Department of Civil and Environmental Engineering, Duke University

Event Details

Speaker invited by

Prof. Dr. Rémi Abgrall

Abstract

Scientific computing is routinely assisting in the design of systems or components, which have potentially very complex shapes. In these situations, it is often underestimated that the mesh generation process takes the overwhelming portion of the overall analysis and design cycle. If high order discretizations are sought, the situation is even more critical. Methods that could ease these limitations are of great importance, since they could more effectively interface with meta-algorithms from Optimization, Uncertainty Quantification, Reduced Order Modeling, Machine Learning, and Artificial Neural Networks, in large-scale applications. Recently, immersed/embedded/unfitted boundary finite element methods (cutFEM, Finite Cell Method, Immerso-Geometric Analysis, etc.) have been proposed for this purpose, since they obviate the burden of body-fitted meshing. Unfortunately, most unfitted finite element methods are also difficult to implement due to: (a) the need to perform complex cell cutting operations at boundaries, (b) the necessity of specialized quadrature formulas on cut elements, and (c) the consequences that these operations may have on the overall conditioning/stability of the ensuing algebraic problems. This talk introduces a simple, stable, and accurate unfitted boundary method, named “Shifted Boundary Method” (SBM), which eliminates the need to perform cell cutting operations. Boundary conditions are imposed on the boundary of a “surrogate” discrete computational domain, specifically constructed to avoid cut elements. Appropriate field extension operators are then constructed by way of Taylor expansions (or similar operators), with the purpose of preserving accuracy when imposing boundary conditions. An extension of the SBM to higher order discretizations will also be presented, together with a summary of the numerical analysis results. The SBM belongs to the broader class of Approximate Boundary Methods, a less explored or somewhat forgotten class of algorithms, which however might have an important role in the future of scientific computing. The performance of the SBM is tested on large-scale problems selected from linear and nonlinear elasticity, fluid mechanics, shallow water flows, thermos-mechanics, porous media flow, and fracture mechanics.

The Shifted Boundary Method: How Approximate Boundaries Can Help in Complex-Geometry Computations

HG E 1.2

8 May 2024
16:30-17:30

Prof. Dr. Maarten de Hoop
Rice University

Event Details

Speaker invited by

Prof. Dr. Habib Ammari

Abstract

We present results pertaining to selected inverse problems associated with seismology on Earth, Mars and Saturn. We focus on geometrical or travel time data originating from the propagation of singularities and the spectra corresponding with normal modes. For terrestrial or rocky planets we highlight recent insights with generic anisotropic elasticity, and for gas giants we reveal the accommodation of the equations of state all the way up to their boundaries. We briefly touch upon whether information on uniqueness of inverse problems is encoded in the data.

Geometric and spectral inverse problems for terrestrial planets and gas giants

HG E 1.2

15 May 2024
16:30-17:30

Dr. Leonardo Zepeda-Nunez
Google Research, USA

Event Details

Speaker invited by	Prof. Dr. Siddhartha Mishra

Title T.B.A.

HG E 1.2

22 May 2024
16:30-17:30

Prof. Dr. Dirk Pauly
TU Dresden

Event Details

Speaker invited by	Prof. Dr. Ralf Hiptmair
Abstract	We study a new notion of trace and extension operators for abstract Hilbert complexes.

Traces for Hilbert Complexes

HG E 1.2

29 May 2024
16:30-17:30

Prof. Dr. Ivan Trapasso
Politecnico di Torino

Event Details

Speaker invited by

Prof. Dr. Rima Alaifari

Abstract

In this talk we provide a concise overview of the fundamental principles underlying harmonic analysis in phase space. The roots of this vibrant field of modern Fourier analysis are to be found at the crossroads of signal analysis, mathematical physics, representation theory and analysis of partial differential equations. The key idea is to exploit a dictionary of oscillating wave packets (or equivalently, the combined structure of translations and modulations or dilations) to investigate properties of functions, distributions and operators in terms of suitable companion phase space representations. Addressing time and frequency/scale on the same level presents both advantages and challenges due to the uncertainty principle. In essence, time and frequency exhibit a somewhat dual nature as variables, hence the efforts to handle them concurrently are ultimately directed to keep track of the multifaceted manifestations of their entanglement. We will delve into these issues, whose origins date back to the foundations of quantum mechanics, and show how they continue to stimulate insightful research in analysis. Lastly, we will offer a taste of applications of these techniques to some problems motivated by the current challenges of data science, mostly in order to convey the message that the principles of time-frequency analysis are ubiquitous, hence adopting a phase space perspective can provide a versatile framework to explore problems from pure and applied mathematics.

Explorations in wave packet analysis

HG E 1.2

25 September 2024
16:30-17:30

Dr. Martin Averseng
Université d’Angers

Event Details

Speaker invited by	Prof. Dr. Ralf Hiptmair

Title T.B.A.

HG ? ?

9 October 2024
16:30-17:30

Prof. Dr. Christinel Mardare
Sorbonne Université

Event Details

Speaker invited by	Stefan Sauter

Title T.B.A.

HG E 1.2

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