Does anybody know how to construct and implement LU-SGS (Low-Upper Symmetric Gauss-Seidel) method? Any comments are welcome. Thanks in advance. Wu

Hi there. Have you tried to look in the Numerical Recipes?

Press, Flannery, Teukolsky and Vetterling, "Numerical Recipes: The Art of Scientific Computing" (Cambridge University Press, New York, 1986). Also 1987, 1988 and probably even 1998 or so (just check in your library).

This is a good book and something about Matrix triangulation (lower upper) and Gauss-Seidel methods is certainly in there.

In which department are you ? Aero ? The book is certainly in the Physics Library.

Cheers, Patrick.

The good articles about LU/SGS are:

W.R.Briley, S.S.Neerarambam & D.L. Whitfield, Implicit LU/AF schemes for incompressible flows//J. Comput. Phys. 128, 32-42 (1996);

S.E.Rogers & D.Kwak//AIAA J. 28, 253 (1990);

S.E.Rogers D.Kwak & C.Kiris//AIAA J. 29, 603 (1991)

Best wishes

I am not sure if you are implementing LU-SGS on structured mesh or unstructured one. In the former case, everything is quite straight-forward, since the mesh can serve as the dividing line between upper and lower pllanes. You can refer to one paper by Jameson in 1987(AIAA Journal, Vol.25,No 7).

If you are implementing LU-SGS on unstructured mesh, you will have much more work to to. You have to color the mesh first, which will be the dividing line. Nakahashi(AIAA Journal, Vol.36, No.3) first implemented LU-SGS on unstructured mesh, at the same time, another company(Amtec Inc, AIAA-96-0167, Tecplot is its main product) used the method in their commercial software. The idea is not complex, since I am now using LU-SGS in Hybrid code.

I am sorry for I cannot give you more detailed information, since I am preparing the final exam these days. Contact me if you have further question.

Guoping