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 student December 18, 2006 00:31

strongly implicit method

sir,

I don't understand the SIP (http://en.wikipedia.org/wiki/Stone_method). what does N represent

Ax = (M-N)x = (LU-N)x = b

in the above equation A and b are known values , what is the need of iteration here.

 zxaar December 18, 2006 00:34

Re: strongly implicit method

A is known but finding Ainv is very difficult, so we prefer iterating. (to know x you need to know Ainv).

 student December 18, 2006 02:33

Re: strongly implicit method

 zxaar December 18, 2006 02:48

Re: strongly implicit method

on cfd-online, in the wiki there is a section on numerical methods, there you will find the link about stone's method. Read that.

 NeaZen December 18, 2006 05:30

Re: strongly implicit method

A contains 5 diagonals (Poisson equation discretisation result via the 5 points scheme).

If we try to performe the incomplete LU decomposition, L and U will contain 3 diagonals each, but the multiplication will produce M with 7 diagonals, so N must contain at minimum 2 diagonals of M that correspond to zero diagonals of A.

So M = L*U and M-N = A

 student December 19, 2006 00:50

Re: strongly implicit method

yes i got 7 diagonals. with L has 3 diagonals, U 2 diagonals the additional two diagonals are stored in N matrix. Could you please expalin how to proceed after this. all are sparse matrix, so how to solve this equation.

 NeaZen December 19, 2006 07:26

Re: strongly implicit method

The best advice I can give you is to look for this book "Computational methods for Fluid Dynamics", Ferziger & Peric, the SIP is clearly explained and you also can download book codes.

Email me if you have difficulties to find them.

 student December 19, 2006 07:56

Re: strongly implicit method