[petsc-users] Multigrid with PML

[Sanjay Govindjee]

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>.

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 
> <mailto: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 <mailto: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

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