Zurich Colloquium in Applied and Computational Mathematics

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20 November 2024
16:30-17:30

Prof. Dr. Carlos Jerez-Hanckes
Universidad Adolfo Ibañez, Santiago, Chile

Event Details

Speaker invited by

Prof. Dr. Ralf Hiptmair

Abstract

In this talk, we will focus on solving time-harmonic, acoustic, elastic and polarized electromagnetic waves scattered by multiple finite-length open arcs in unbounded two-dimensional domain. We will first recast the corresponding boundary value problems with Dirichlet or Neumann boundary conditions, as weakly- and hyper-singular boundary integral equations (BIEs), respectively. Then, we will introduce a family of fast spectral Galerkin methods for solving the associated BIEs. Discretization bases of the resulting BIEs employ weighted Chebyshev polynomials that capture the solutions' edge behavior. We will show that these bases guarantee exponential convergence in the polynomial degree when assuming analyticity of sources and arc geometries. Numerical examples will demonstrate the accuracy and robustness of the proposed methods with respect to number of arcs and wavenumber. Moreover, we will show that for general weakly- and hyper-singular boundary integral equations their solutions depend holomorphically upon perturbations of the arcs' parametrizations. These results are key to prove the shape holomorphy of domain-to-solution maps associated to BIEs appearing in uncertainty quantification, inverse problems and deep learning, to name a few applications. Also, they pose new questions you may have the answer to!

New Insights on Wave Scattering by Multiple Open Arcs: Lightning-Fast Methods and Shape Holomorphy

HG G 19.2

4 December 2024
16:30-17:30

Prof. Dr. Gui-Qiang G. Chen
University of Oxford

Event Details

Speaker invited by	Prof. Dr. Habib Ammari

Title T.B.A.

HG G 19.2

11 December 2024
16:30-17:30

Dr. Federico Pichi
SISSA, Trieste, Italy

Event Details

Speaker invited by	Prof. Dr. Christoph Schwab

Title T.B.A.

HG G 19.2

18 December 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 G 19.2

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

Title T.B.A.

HG G 19.2

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