# Multigrid methods

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

 April 5, 2002, 02:16 Multigrid methods #1 Amith Guest   Posts: n/a Hi, I was curious to know why Multi grid methods cannot be applied to hyperbolic equations and is applicable only for elliptic equations. Regards, Amith

 April 5, 2002, 08:38 Re: Multigrid methods #2 andy Guest   Posts: n/a Multigrid methods do get applied to hyperbolic equations and they often accelerate the convergence rate to some degree. However, they almost never approach the performance achievable when used with elliptic equations. The performance of a multigrid method for a particular equation or, more usually in CFD, set of equations is dependent on the details of the various components in the multigrid scheme. That is, the prolongation method, the restriction method, the cycling strategy, the coupling strategy, the smoother, etc... A particular scheme can work extremely well for one set of equations and simply fail for another set. The reasons for good performance or bad are going to vary from scheme to scheme and set of equations to set of equations. The pat answer to your question is the lack of smoothness in the solutions to hyperbolic equations compared to elliptic equations. See any multigrid book for a description why this property is important for a multigrid scheme. Nonetheless, there are usually things one can do in practice to ease the situation and get some acceleration of convergence.

 April 5, 2002, 16:43 Re: Multigrid methods #3 Frederic Felten Guest   Posts: n/a Hi there, For elliptic problems (like a pressure poisson equation), the solutions is driven by the boundary conditions (this is not the case for hyperbolic problems). The regular iterative methods are slow to propagate the information troughout the domain especially for the low frequencies. The multigrid method is then a fast way of get rid of this slow convergence process. Sincerely, frederic Felten.

 April 5, 2002, 23:50 Re: Multigrid methods #4 Neale Guest   Posts: n/a You could use a multigrid method on a hyperbolic equation, but it probably would not help all that much. Multigrid tends to do well on elliptic problems because they are non-local. In particular it's really good at smoothing out long wavelength errors over the entire domain. Hyperbolic problems tend to behave like wave propagation, which can only propagate at a specific speed. Wave propagation is not non-local like diffusion, in that influence effects are only felt after a specific amount of time. Diffusion acts everywhere all at once. As a result, standard iterative techniques, such as point Jacobi, or point Guass-Siedel, or ILU, etc... without multigrid, will tend to do just as well as multigrid on pure hyperbolic problems. Neale.

 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 mnabi Main CFD Forum 8 July 11, 2009 20:21 Lionel S. Main CFD Forum 10 April 20, 2007 09:22 sureshkumar Main CFD Forum 0 June 9, 2006 01:20 kenn Main CFD Forum 2 July 18, 2004 18:28 Paulo Zandonade Main CFD Forum 9 May 24, 1999 08:10

All times are GMT -4. The time now is 07:24.