Институт математики и математического моделирования

“Analysis and Applied Mathematics” Еженедельный онлайн семинар 29

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Date: Tuesday, April 9, 2024
Time: 14.00-15.00 (Istanbul) = 13.00-14.00 (Ghent) = 16.00-17.00 (Almaty)

Zoom link: https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaH- lDaVYrN3l5bzJVQT09,

Conference ID: 667 827 0445, Access code: 1

Speaker:
Prof. Dr. Fatih Ecevit
Boğaziçi University, Istanbul, Türkiye
Title: Computing the infinite tail in the Neumann series repre-sentation 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 bound-ary 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 un-derlying 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 (depend-ing on the geometry) partial sum of the Neumann series, and computation of the remaining infinite tail in just one solve 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 dis-cuss 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

Biography:

Fatih Ecevit received his PhD in Mathematics from University of Minnesota, Twin Cities in 2005. He was a postdoc in the Scientific Computing Group at the Max Plank Institute of Mathematics in the Sciences, Leipzig, from 2005-2007. He has since been working at Boğaziçi University, Department of Mathematics. Fatih Ecevit’s research interests lie in clas-sical analysis, partial differential equations, numerical analysis, integral equations, and semiclassical/microlocal analysis with particular emphasis on high-frequency scattering problems.

Kazakh Mathematical Journal

“Analysis and Applied Mathematics” Еженедельный онлайн семинар 29

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