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SUMMARY:Revistin Multigrid for the Helmholtz Problem
DTSTART:20191016T100000
DTEND:20191016T110000
DTSTAMP:20260406T214401Z
UID:3848564bcd784fe1094a09ae0f7aec8e54986bd514f17c3c210c5fdc
CATEGORIES:Conferences - Seminars
DESCRIPTION:Adem KAYA\nIt is well known that standard multigrid algorithms
  are ineffective to solve the discrete Helmholtz problems and there are se
 veral well-written articles that try to interpret this difficulty.\n\n\nIn
  this presentation\, we reconsider the multigrid for the discretizations o
 f the Helmholtz problem and bring new insights. We propose a new simple Fo
 urier analysis (SFA) which is different from the existing one in literatur
 e\, and very easy to understand. With SFA\, we obtain all spectral informa
 tion of the iteration matrix of the two-grid for a generic symmetric tridi
 agonal matrix. Then\, we examine multigrid for the Helmholtz problem in 1D
  as its discretizations with Dirichlet boundary condition\, give symmetric
  tridiagonal matrices. Our analyses show that there are fundamental issues
  in the interpretation of the multigrid for the Helmholtz problem. Moreove
 r\, we reinterpret the problematic coarse levels for the multigrid and bri
 ng a restriction on the coarse levels. This restriction reduces the comput
 ational cost for the existing multigrid algorithms\, significantly. Based 
 on this observation\, we propose a convergent multigrid algorithm.
LOCATION:MA B1 524 https://plan.epfl.ch/?room==MA%20B1%20524
STATUS:CONFIRMED
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