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 Tareq Al-shaalan December 21, 1998 05:38

Single Grid-Multi grid

I would like to know the difference between single grid and multi grid. Would there some body to explain the difference between them.

 P.Jawahar December 21, 1998 07:31

Re: Single Grid-Multi grid

Multigrid is basically a convergence acceleragion technique. It is an iterative procedure to get a numerical solution of a problem on a "given grid" by repetitive iterations with a hierarchy of coarser grids. It is based on the observation that global features of the solution which create problems on a fine grid can be resolved and inexpensively processed on coarser grids.

The solver performes iterative sweeps on both fine as well as coarse grids with intergrid transfer of information; each grid supplies corrections to the governing equations of the next coarser grid and additionally it provides corrections to the approximate solution of the next finer grid. So, typically, multigrid is scheduled as V-CYCLE, W-CYCLE etc.,.

Hope it helps !

Jawahar

 Tareq Al-shaalan December 26, 1998 01:11

Re: Single Grid-Multi grid

Mary Xmas and happy holidays

Doses any body know of any reference that explains Single Grid and Multi grid in details.

 P.Jawahar December 26, 1998 02:37

Re: Single Grid-Multi grid

Check out the following references: Let me warn you in the first place that they may not be in proper order !

Spekreijse, S.P., Multigrid solution to the steady Euler equations, Ph.D Thesis, Centre for Mathematics and Computer Science, Amsterdam, 1987.

Koren, B.,Koren, B., Multigrid and defect correction for the steady Navier-Stokes equations,J. Comput. Phys.,} 1990, 87, 25-46

W.L.Briggs "A Multigrid Tutorial", SIAM 1987

W.Hackbusch, "Multigrid methods and applications", Springer-Verlag, Berlin 1985

D.C. Jespersen, " Design and implementation of a multigrid code for the Euler equations". Appl. Math. Comput., 13, 357-374, 1983.

G.Shaw and P.Wesseling, " Multigrid method for the compressible Navier-Stokes equations", Lecture Notes in Physics, 264, Springer Verlag, Berlin 1986

I think P.Wesseling has written a book on Multigrid methods; (I may be wrong also, but checkout his recent work )

R.Radespiel and R.C.Swanson, "Progress with multigrid schemes for hypersonic flow problems", JCP, 116, 103-122, 1995.

Also there is a conference held exclusively for Multigrid methods called; " COPPER MOUNTAIN CONFERENCE ON MULTIGRID METHODS". Check-out NASA Conference proceedings !

Also, check out VKI Lecture series.

You can check ICASE, NASA-technical report servers and some of the following sites on internet:

University of Dundee homepage contains some information and links to Multigrid technology and relted software. You can find it at:

http://www.mcs.dundee.ac.uk:8080/software/index.html

Also Check-out recent research work by D.J.Mavriplis at ICASE on Unstructured Multigrid:

http://www.icase.edu/newresearch/des/advmth.html

Good Luck,

Merry X'mas and Happy New Year

Jawahar

 Donald Hawken January 9, 1999 18:53

Re: Single Grid-Multi grid

Hi Tareq

Try looking in the book "More C Tools for Scientists and Engineers" by Louis Baker, published by McGraw-Hill 1991 for a section on Multigrid Methods including a program listing.

Don Hawken WWW home page http://www2.magmacom.com/~dhawken (last updated on December 1, 1998, demo CFD software)

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