# Help about the preconditioner in gmres method

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

 July 2, 2008, 03:49 Help about the preconditioner in gmres method #1 Dan Gao Guest   Posts: n/a Hi, all, I am importing a implicit time method to my 3D NS finite difference code. I used the Matrix-free method to get the Jaccobi matrix-vector product, and the sparse linear equations are solved by gmres method. Now I am in trouble in constructing a preconditioner for my finite difference code. I hope the preconditioning method is similar with the matrix-free method, that means only the preconditioner-vector product needed. I hope someone can suggest me how to construct a preconditioner for my finite difference code. I read some papers about how to get the preconditioner for finite volume method. But I can not understand it and import them to the finite difference method. I don't know I describe the question clearly. I am poor in English. Thanks for your any help in advance .

 July 2, 2008, 04:50 Re: Help about the preconditioner in gmres method #2 Tom Guest   Posts: n/a It's not quite the same. You need to write a subroutine that calculates (approximately) an estimate of the increment for Newton's method. One choice is to use something like the SIMPLE algorithm but rearranged to yield the "correct" increments. Knolls & Keyes (correct spelling?) have written papers on this. One possible choice, which would avoid the need to construct the preconditioner, would be to wrap a multigrid solver around around the call to GMRES.

 July 3, 2008, 08:41 Re: Help about the preconditioner in gmres method #3 Jed Guest   Posts: n/a I also recommend Knoll & Keyes 2004. Let's suppose we are doing left preconditioning so we would like P^{-1} A to be approximately the identity. The trouble is that P^{-1} usually needs to be dense. Storing a dense matrix is not going to work and unless you have a fast solver for a similar problem (which generally requires a really nice domain) then you you'll want to actually form a preconditioning matrix P because preconditioners (such as ILU(k), AMG, DD) normally want matrix entries. The big win is that the preconditioning matrix can come from simpler physics and/or lower order discretization so it may have fewer entries and be easier to compute than the full Jacobian. Also, the preconditioner can often be lagged (don't recompute the preconditioner every Newton step) which further reduces assembly cost. When you do have a fast solver for simpler physics, then by all means, try it. This is called `physics based preconditioning' in Knoll & Keyes. Note that linear multigrid as a preconditioner for a Krylov method is generally faster than nonlinear multigrid.

 July 5, 2008, 01:18 Re: Help about the preconditioner in gmres method #4 Dan Gao Guest   Posts: n/a Thank Tom and Jed for your help. I will try it.

 Thread Tools Display Modes Linear Mode

 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 OffTrackbacks are On Pingbacks are On Refbacks are On Forum Rules

 Similar Threads Thread Thread Starter Forum Replies Last Post Andyjoe Open Source Meshers: Gmsh, Netgen, CGNS, ... 13 March 14, 2012 05:35 Anorky FLUENT 0 April 27, 2010 10:55 m-fry Main CFD Forum 1 April 20, 2010 14:40 D.S.Nasan Main CFD Forum 6 September 4, 2008 02:08 ztdep Main CFD Forum 1 August 12, 2008 06:28

All times are GMT -4. The time now is 10:56.