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SUMMARY:New Insights on High Frequency Wave Scattering by Multiple Open Ar
 cs: Exponentially Convergent Methods and Shape Holomorphy - Carlos Jerez H
 anckes (University of Bath)
DTSTART:20250515T140000Z
DTEND:20250515T150000Z
UID:TALK228775@talks.cam.ac.uk
CONTACT:Georg Maierhofer
DESCRIPTION:In this talk\, we focus on the scattering of time-harmonic aco
 ustic\, elastic\, and polarized electromagnetic waves by multiple finite-l
 ength open arcs in an unbounded two-dimensional domain. We begin by reform
 ulating the corresponding boundary value problems with Dirichlet or Neuman
 n conditions as weakly and hypersingular boundary integral equations (BIEs
 )\, respectively. We then introduce a family of fast spectral Galerkin met
 hods for solving these BIEs. The discretization bases are built from weigh
 ted Chebyshev polynomials that accurately capture the solutions’ edge be
 havior. Under the assumption of analyticity of the sources and arc geometr
 ies\, we show that these bases yield exponential convergence with respect 
 to the polynomial degree.\n\nNumerical examples will illustrate the accura
 cy and robustness of the proposed methods\, with respect to both the numbe
 r of arcs and the wavenumber. Additionally\, we demonstrate that\, for gen
 eral weakly and hypersingular BIEs\, the solutions depend holomorphically 
 on perturbations of the arc parametrizations. These results are crucial fo
 r establishing the shape holomorphy of domain-to-solution maps arising in 
 boundary integral equations\, with applications in uncertainty quantificat
 ion\, inverse problems\, and deep learning\, among others. They also raise
  new questions—some of which you may have the answer to!
LOCATION:Centre for Mathematical Sciences\, MR14
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