CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > General Forums > Main CFD Forum

algebraic multigrid vs geometric multigrid

Register Blogs Community New Posts Updated Threads Search

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   December 30, 2012, 16:01
Question algebraic multigrid vs geometric multigrid
  #1
Senior Member
 
Anna Tian's Avatar
 
Meimei Wang
Join Date: Jul 2012
Posts: 494
Rep Power: 16
Anna Tian is on a distinguished road
Hi,

What is the advantages and disadvantages of Algebraic Multigrid compared with Geometric Multigrid? From my experience, algebraic multigrid is much slower than geometric multigrid. Is that always true? Why?
__________________
Best regards,
Meimei
Anna Tian is offline   Reply With Quote

Old   January 2, 2013, 07:43
Default
  #2
New Member
 
Join Date: Jan 2013
Posts: 3
Rep Power: 13
ignatius is on a distinguished road
Hi Anna,
Algebraic multigrid is supposed to work better with complex geometries and also with highly anisotropic problems. It would be nice if you can get somewhere the book "Multigrid" from Trottemberg, there you can find a really good explanation about it, it has an appendix about algebraic multigrid.
ignatius is offline   Reply With Quote

Old   June 13, 2013, 12:55
Question
  #3
Senior Member
 
Anna Tian's Avatar
 
Meimei Wang
Join Date: Jul 2012
Posts: 494
Rep Power: 16
Anna Tian is on a distinguished road
Quote:
Originally Posted by ignatius View Post
Hi Anna,
Algebraic multigrid is supposed to work better with complex geometries and also with highly anisotropic problems. It would be nice if you can get somewhere the book "Multigrid" from Trottemberg, there you can find a really good explanation about it, it has an appendix about algebraic multigrid.
Could you give a basic conclusion about what are the advantages of geometric multigrid method compared with algebraic multigrid method? Is it always faster?
__________________
Best regards,
Meimei
Anna Tian is offline   Reply With Quote

Old   June 17, 2013, 23:28
Default
  #4
Senior Member
 
cdegroot's Avatar
 
Chris DeGroot
Join Date: Nov 2011
Location: Canada
Posts: 414
Rep Power: 18
cdegroot is on a distinguished road
To clarify, geometric multigrid actually discretizes the problem on a series of grids whereas algebraic multigrid simply works with the linear system. When working with unstructured grids it is really difficult to define a series of meshes for geometric multigrid so algebraic multigrid is usually used instead. It's not really a matter of speed, more so one of convenience.
cdegroot is offline   Reply With Quote

Old   June 18, 2013, 04:58
Default
  #5
Senior Member
 
sbaffini's Avatar
 
Paolo Lampitella
Join Date: Mar 2009
Location: Italy
Posts: 2,192
Blog Entries: 29
Rep Power: 39
sbaffini will become famous soon enoughsbaffini will become famous soon enough
Send a message via Skype™ to sbaffini
The main fact about the geometric multigrid is that, by discretizing the problem on each grid level, the non-linearity is not lost, say, for Navier-Stokes equations. I don't know if for linear problems there is yet some advantage in the geometric approach.
sbaffini is offline   Reply With Quote

Old   June 18, 2013, 06:03
Default
  #6
Senior Member
 
duri
Join Date: May 2010
Posts: 245
Rep Power: 17
duri is on a distinguished road
Geometric multigrid can be used for both implicit and explicit solvers. Geometric multigrid construction is quite difficult for unstructured meshes. There are many ways to construct coarser grid for GMG. I have coded agglomeration technique for GMG which is quite generic. In case of anisotropy coarse grid construction plays an important role. There is no issue of linearity and non-linearity in case of geometric multigrid, as only the mesh changes but the system is still non-linear. There may be loss in restriction and prolongation operators (not sure of this).

Algebraic multigrid can be applied only for implicit methods. Algebraic method works on the matrix with the spirit of geometric multigrid concept. Since matrix operation is linear, AMG is basically linear. AMG is easy to implement doesn't need complex geometry coarsening. Anisotropy can be controlled by selecting the appropriate coarse level matrix.
duri is offline   Reply With Quote

Reply


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
GAMG = geometric algebraic multigrid? schmittp54 OpenFOAM Programming & Development 1 December 11, 2010 08:25
Grid Block Interface / Algebraic Multigrid Harun CFX 0 August 5, 2007 17:06
Black Box Algebraic Multigrid Neazen Main CFD Forum 0 June 4, 2007 08:10
Seeking Algebraic Multigrid Code Anna Main CFD Forum 1 May 11, 2006 21:05
How to update polyPatchbs localPoints liu OpenFOAM Running, Solving & CFD 6 December 30, 2005 18:27


All times are GMT -4. The time now is 13:32.