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SUMMARY:High order convergence of the PML method for periodic surface scat
 tering problems - Ruming Zhang (Karlsruhe Institute of Technology (KIT))
DTSTART:20230418T130000Z
DTEND:20230418T134500Z
UID:TALK198718@talks.cam.ac.uk
DESCRIPTION:The main task in this talk is to prove that the perfectly matc
 hed layers (PML) method has high order converge with respect to the PML pa
 rameter\, for scattering problems with periodic surfaces. A linear converg
 ence has already been proved for the PML method for scattering problems wi
 th rough surfaces in a paper by S.N. Chandler-Wilder and P. Monk in 2009. 
 At the end of that paper\, three important questions are asked\, and the t
 hird question is if exponential convergence holds locally. In this talk\, 
 we answer this question for a special case\, i.e.\, scattering problems wi
 th periodic surfaces. The main idea of the proof is to apply the Floquet-B
 loch transform to write the problem into an equivalent family of quasi-per
 iodic problems\, and then study the analytic extension of the quasi-period
 ic problems with respect to the Floquet-Bloch parameters. Then the Cauchy 
 integral formula is applied for piecewise analytic functions to avoid line
 ar convergent points. Finally the exponential convergence is proved for al
 most all 2D cases and 3D cases with small wavenumbers\, and high order con
 vergence is proved for 3D cases with larger wavenumbers.
LOCATION:Seminar Room 1\, Newton Institute
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