Re: SOR technique for semiconductor continuity equation


In article <1143538206.026673.269410@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"cmj" <council.tax@xxxxxxxxx> writes:
Ah, thank you for that. I know conditions 1 and 3 are met and I
suspect condition 2 is also met, so I will try that out.

Does optimal omega theory mean that I can use w_opt = 2 / ( 1 +
sin(pi/(n+1)) ) with n the iteration step if I use a 2 dimensional
square lattice?

And finally (sorry for asking so many questions), Will this value of
omega work for the 4th and 5th lines of the above matrix, where the
equations are respectively:

c7.n3 - (c8.n4 +k.n4.n5) = 0
c10.n6 - (c9.n5 + k.n4.n5) = 0

It just seems odd that the optimum omega for these two equations should
be the same as the optium omega for all the other equations (which are
essentially the same).

Many thanks for all your help,

Chris


the optimal omega is for the system as a whole, there is only _one_ omega
(for a positive definite system you could use individual omega's for the
different rows, but there is no theory how to optimize here )
but your value sin(pi/(n+1)) n=dimension (not step nr.!)
will not be valid. for the matrix
A=tridiag(-1,2,-1)
it is
omega_best=2/(1+sin(pi/(n+1)))
in general the formula is
omega_best = 2/(1+sqrt(1-mu^2))
where mu is the spectral radius of the matrix inverse(diag(A))*(A-diag(A))
(the matrix of the Jacobi-iterative scheme)
normally omega_best is computed adaptively in the iteration, beginning
with omega=1, after a considerable number of iterations the spectral
radius of the gauss-seidel iteration (which is mu^2 under the conditions
named) is extracted and then omega_best is computed and used.
see Hageman&Young: applied iterative methods
hth
peter
.

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