[Turkmath:6433] The Announce of Weekly Online Seminar “Analysis and Applied Mathematics"

[Allaberen Ashyralyev]

Dear Colleagues!
You are cordially invited to the  Weekly Online Seminar “Analysis and
Applied Mathematics” on
*Date*: Tuesday, April 9, 2024
*Time:* 14.00-15.00 (Istanbul) = 13.00-14.00 (Ghent) = 16.00-17.00 (Almaty)
  Place: Zoom link:
https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaHlDaVYrN3l5bzJVQT09,
Conference ID: 667 827 0445, Access code: 1
*Speaker: *  Assoc.Prof. Dr. Fatih Ecevit
*Boğaziçi University, Istanbul, Türkiye *
*Title: * Computing the infinite tail in the Neumann series representation
of high-frequency multiple scattering problems
*Abstract:* We consider the high-frequency multiple scattering problem in
the exterior of several convex obstacles. In this context, we review (1)
the single scattering Galerkin boundary element methods (BEM) for the
frequency independent approximation of the solutions, and (2) the Neumann
series reformulation of multiple scattering problems along with the
extension of single scattering Galerkin BEM to this case. These strategies
provide the guidelines for the frequency independent approximation of
multiple scattering iterations. However, important additional issues arise
in connection with the Neumann series as it may converge quite slowly or
even diverge depending on the underlying geometrical configuration. In this
connection, we present our ongoing work on Ray stabilized Galerkin BEM
which still uses the Neumann series reformulation even if it may diverge.
Specifically, our approach is based on the calculation of a sufficiently
large (depending on the geometry) partial sum of the Neumann series, and
computation of the remaining infinite tail in just one solution through the
construction of Ray-stabilized Galerkin BEM. Time permitting, we also
present ongoing work on its Bayliss-Turkel type approximation of the
high-frequency scattering amplitude based on the method of stationary
phase, and discuss the extension of this approach to multiple scattering
scenarios in conjunction with the Ray-stabilized Galerkin BEM.
 *Abstracts and forthcoming talks can be found on our webpage*
https://sites.google.com/view/aam-seminars
With my best wishes
*Prof. Dr. Allaberen Ashyralyev *
*Department of Mathematics, Bahcesehir University,**34349**, Istanbul,
Turkiye*
*Peoples' Friendship University of Russia (RUDN University),** Ul Miklukho
Maklaya 6, Moscow 117198, Russian Federation *
*Institute of Mathematics and Mathematical Modelling, 050010, Almaty,
Kazakhstan*
*e-mail: allaberen.ashyralyev at bau.edu.tr
<allaberen.ashyralyev at neu.edu.tr> and **aallaberen at gmail.com
<aallaberen at gmail.com> *
 http://akademik.bahcesehir.edu.tr/web/allaberenashyralyev

https://sites.google.com/view/aam-seminars

https://ejaam.org/editorial.html

*icaam-online.org <http://icaam-online.org>*

*https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1
<https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1>*
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