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SUMMARY:Wenzhong Zhang (Southern Methodist University)
DTSTART:20200722T150000Z
DTEND:20200722T160000Z
DTSTAMP:20260423T005812Z
UID:GSMMA/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GSMMA/12/">F
 ast multipole method for Helmholtz equation in layered media</a>\nby Wenzh
 ong Zhang (Southern Methodist University) as part of Global Seminar on Mat
 hematical Modeling and Applications\n\n\nAbstract\nThe fast multipole meth
 od (FMM) has been a revolutionary development in modern computational algo
 rithms for many-body problems\, which reduces the complexity of long-range
  interactions among N particles from O(N^2) to O(N) or O(N log N). In this
  talk we generalize the FMM for Helmholtz equation to handle the layered m
 edia. Our approach starts from the 2-D case. The multipole expansion (ME) 
 and the multipole-to-local translation (M2L) are introduced in the frequen
 cy domain together with theoretical analysis showing their exponential con
 vergence using the Cagniard--de Hoop transform. The analysis further sugge
 sts the FMM framework for layered media should use polarized sources for t
 he far-field separation. Finally we apply the FMM to the 3-D layered probl
 em and discuss the numerical result. This is a joint work with Bo Wang and
  Wei Cai.\n\nMeeting ID: 970 1588 0121\nPasscode: 835247\n
LOCATION:https://researchseminars.org/talk/GSMMA/12/
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