CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > Software User Forums > Siemens

AMG method?

Register Blogs Members List Search Today's Posts Mark Forums Read

Like Tree1Likes
  • 1 Post By Hubert Janocha

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   September 14, 2005, 11:44
Default AMG method?
  #1
HADD
Guest
 
Posts: n/a
Hi

I can't find any information about method using for AMG technique. I mean, is it Gauss-Seidel method or CG or something else? As i understand, AMG is general technique of solving system of linear equation, but it should includes methods mentioned above. If my opinion is wrong, please correct me

Thanks in advance

  Reply With Quote

Old   September 14, 2005, 18:42
Default Re: AMG method?
  #2
staruser
Guest
 
Posts: n/a
AMG means algebraic multi grid. It's a method to solve equations systems effectively. You solve your equation system on different meshes (fin -> coarse). Since you have different frequency of errors on differ mesh density, you can solve low frequency errors on coarse grids more efficently. Mayby you should have a look at the theory behind it. Look for litterature by Achi Brandt and Hackbusch. It normally needs a "pre conditioner" e.g. CG (used in STAR-CD). If you can solve your equation system farily good after only a few CG iterations, it would be too expensive to start a AMG process, hence in STAR-CD AMG is only applied for the pressure equation which normally needs a lot of itersations. And yes, it is different from Gauss Seidel or CG.
  Reply With Quote

Old   September 15, 2005, 14:10
Default Re: AMG method?
  #3
HADD
Guest
 
Posts: n/a
Thank you very much for your detailed answer!

Could you, please, answer some more questions

1. You wrote: "You solve your equation system on different meshes (fin -> coarse)"

But what the method is used for solving the system of linear equation on, for example, coarse grid in STAR-CD? Is it any of iterative methods or direct?

2. Could you give any link for Achi Brandt and Hackbusch books?

Thanks in advance

  Reply With Quote

Old   September 15, 2005, 16:43
Default Re: AMG method?
  #4
staruser
Guest
 
Posts: n/a
1) It's allways an iterative method. Direct methods would need too much memory. The coarser meshes are virtual and are created authomatically by STAR-CD, hence you need to allocate more memory during the solver process. You can observe this in v3.15a, where the approximate memory usage is give after "starlink -x..."; during the run, more memory will be allocated.

2) http://www.wisdom.weizmann.ac.il/~achi/ and (e.g.) Hackbush, W., Multi-Grid Methods and Applications, Springer-Verlag, Berlin(1985). Look for "Hackbush multi" at google.
  Reply With Quote

Old   September 15, 2005, 19:01
Default Re: AMG method?
  #5
zxaar
Guest
 
Posts: n/a
imagine that you take some neighbouring cells and join them and make one single volume. So this way you can create coarser control volume(u get a coarse mesh). Now you can again merge these coarse volumes and create another coarser mesh. You can do it and create some coarser meshes, say 4-5 meshes.

A typical multigrid cycle starts at a finest level. The fine level solution is then transferred to next coarser level, this is called restriction. After some relaxation cycles this coarse level the solution is then restricted to next coarser level until the coarsest level is reached. The solution obtained at the coarsest level is than interpolated back to finer level, this step is called prolongation. The solution from this finer level is interpolated to next finer level after some relaxation iterations, called post multigrid sweeps. The solution is prorogated till the finest level is reached. The whole process is repeated until satisfactory convergence is reached.
  Reply With Quote

Old   September 16, 2005, 12:19
Default Re: AMG method?
  #6
HADD
Guest
 
Posts: n/a
Thanks a lot for yours explanations! its help me very much!

But I don't understand, what concrete iterative method is used in AMG algorithm ( within STAR-CD) ?

For example, in FLUENT documentation I read: " FLUENT solves this linear system using a point implicit (Gauss-Seidel) linear equation solver in conjunction with an algebraic multigrid (AMG) method"

  Reply With Quote

Old   September 16, 2005, 17:23
Default Re: AMG method?
  #7
zxaar
Guest
 
Posts: n/a
i can not speak of starCD, but starCCM+ also uses gauss-seidel, that it, at each level you solve by gauss-seidel solver. Its easy to use with unstructured grids. Fluent also gives an option of using BiCGStab.
  Reply With Quote

Old   September 20, 2005, 18:14
Default Re: AMG method?
  #8
staruser
Guest
 
Posts: n/a
STAR-CD uses CG (conjugate gradient) for pre-conditioning.
  Reply With Quote

Old   September 20, 2005, 23:08
Default Re: AMG method?
  #9
zxaar
Guest
 
Posts: n/a
conjugate gradient are for symmetric metrices, that is for pressure correction equation, this preconditioner is valid, what does it do for other scalars, does it use biCGStab, or anyother similar method?????
  Reply With Quote

Old   September 21, 2005, 10:56
Default Re: AMG method?
  #10
Hubert Janocha
Guest
 
Posts: n/a
Multigrid is a accelleration scheme / procedure for a wide range of quit normal matrix solvers, first of all Gauss Seidel Relaxation. This normal matrix solver is called in multigrid a "smoother".

"Numerical Recipes" gives a good and relativly short explanation (and example fortran and c sources) of what is multigrid. To explain it here even roughly is not possible. If you can understand german language I can give you a documantation, which very easy to understand. But you don't realy need this to know.

What you should know about multigird is:

- only reasonable for steady state problems.

- in 2D solver acceleration of possibly 100 times (depends on the mesh size)

- in 3D acceleration of about 5 to 10 times in optimal configuration and for very big meshes. In StarCD perhaps only 1.5 times (about 1 mill. cells, with good luck). Again this depends strongly on the mesh size.

- has some stability advantage for compressible flows.

- nearly linear convergence behaviour, so it is almost independend of the mesh size (dependent on the smoother). Therefore it becomes more and more advantagous for bigger and bigger meshes.

In the past it was good to overcome weak CPU-performance, but in the future it will be necessary to get convergence at all on extremly big meshes, because every solver becomes weak for a certain mesh size. E.g. the limitation of Gauss Seidel is about 2 mio cells. The solution progress is so small that the values of the cells react mainly only to the changes of the neihgbour cell.

Milovan Peric and Muzaferia are experts in applied Multigrid.
aerosayan likes this.
  Reply With Quote

Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
Comparing between the Fractional step method and the SIMPLE method ghlee Main CFD Forum 1 April 10, 2012 17:59
Finite volume method vs finite difference method? superfool Main CFD Forum 4 October 21, 2006 15:37
Pressure Correction method, Finite Volume Method Seeker01 Main CFD Forum 2 January 13, 2003 03:49
hess-smith method and fvm method yangqing FLUENT 0 March 20, 2002 20:25
Projection method and Block-off method Leo Main CFD Forum 0 June 14, 2001 08:22


All times are GMT -4. The time now is 21:06.