[petsc-users] Multigrid with PML

[domenico lahaye]

Dear Artur, 
  Out of a blend of curiosity and healthy naivity: have you tried complex shifted Laplace as 
a preconditioner? 

  Greetings, Domenico Lahaye.
 
      From: Sanjay Govindjee <s_g at berkeley.edu>
 To: petsc-users at mcs.anl.gov 
 Sent: Friday, July 15, 2016 11:02 AM
 Subject: Re: [petsc-users] Multigrid with PML
   
 I agree, this is an extra hard problem when you add PML to it.  Here is a link to a paper that presents a few tricks applied to some aspects of this problem.
 
 Koyama, T. and Govindjee, S., ``Solving generalized complex-symmetriceigenvalue problems arising fromresonant MEMS simulations with PETSc," in Proceedings in AppliedMathematics and Mechanics, 1141701-1141702 (2008).
 
 http://dx.doi.org/10.1002/pamm.200700206
 
 -sg
 
 On 7/15/16 1:46 AM, Mark Adams wrote:
  
 
 
 On Thu, Jul 14, 2016 at 9:10 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
 

    This is a very difficult problem. I am not surprised that GAMG performs poorly, I would be surprised if it performed well at all.
 
    I think you need to do some googling of   "helmholtz PML linear system solve" to find what other people have used. The first hit I got was this http://www.math.tau.ac.il/services/phd/dissertations/Singer_Ido.pdf and every iterative method he tried ended up requiring MANY iterations with refinement. This is 14 years old so there will be better suggestions out there. One that caught my eye was http://www.sciencedirect.com/science/article/pii/S0022247X11005063
 
 
   Barry
 
 Just looking at the matrix makes it clear to me that conventional iterative methods are not going to work well, many of the diagonal entries are zero and even in rows with a diagonal entry it is much smaller in magnitude than the diagonal entries.
 
 
  Indefinite Helmholtz is hard unless you are not shifting very far. This zero diagonals must come from PML. 
  First get rid of PML and see if you can solve anything to your satisfaction. 
  I have a paper on this, using AMG, and I tried to be inclusive, but I did miss a potentially useful method of adding a complex shift to damp the system. You can Google something like 'complex shift helmholtz damp'.  If you are shifting deep (high frequency Helmholtz), then use direct solvers.   

 > On Jul 13, 2016, at 2:30 PM, Safin, Artur <aks084000 at utdallas.edu> wrote:
 >
   > Dear PETSc community,
 >
 > I am working on solving a Helmholtz problem with PML. The issue is that I am finding it very hard to deal with the resulting matrix system; I can get the correct solution for coarse meshes, but it takes roughly 2-4 times as long to converge for each successively refined mesh. I've noticed that without PML, I do not have problems with convergence speed.
 >
 > I am using the GMRES solver with GAMG as the preconditioner (with block-Jacobi preconditioner for the multigrid solves). I have also tried to assemble a separate preconditioning matrix with the complex shift 1+0.5i, that does not seem to improve the results. Currently I am running with
 >
 >    -ksp_type fgmres \
 >    -pc_type gamg \
 >    -mg_levels_pc_type bjacobi \
 >    -pc_mg_type full \
 >    -ksp_gmres_restart 150 \
 >
 > Can anyone suggest some way of speeding up the convergence? Any help would be appreciated. I am attaching the output from kspview.
 >
 > Best,
 >
 > Artur
 >
   > <kspview>
 
 
  
   
 
 -- 
-----------------------------------------------
Sanjay Govindjee, PhD, PE
Professor of Civil Engineering

779 Davis Hall
University of California
Berkeley, CA 94720-1710

Voice:  +1 510 642 6060
FAX:    +1 510 643 5264
s_g at berkeley.edu
http://www.ce.berkeley.edu/~sanjay
-----------------------------------------------

Books:  

Engineering Mechanics of Deformable 
Solids: A Presentation with Exercises
http://www.oup.com/us/catalog/general/subject/Physics/MaterialsScience/?view=usa&ci=9780199651641
http://ukcatalogue.oup.com/product/9780199651641.do
http://amzn.com/0199651647

Engineering Mechanics 3 (Dynamics) 2nd Edition
http://www.springer.com/978-3-642-53711-0
http://amzn.com/3642537111

Engineering Mechanics 3, Supplementary Problems: Dynamics 
http://www.amzn.com/B00SOXN8JU

-----------------------------------------------
 

  
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20160715/031e2165/attachment-0001.html>