Re: SOR technique for semiconductor continuity equation

cmj wrote:

Pete,

thanks for your help so far, I've got a copy of the book you
recommended in front of me. Unfortunatley something worries me, namely
that the cases mentioned in the book always have matrix elements aij as
constants, whereas in my case they can be variables.

To clarify things, the equation I am trying to solve is as follows:

cn''(x) = 0 (the time independent diffusion equation)

with c = c1 for 0 < x < L/2 and c = c2 for L/2 <= x < L
Dirichlet boundary conditions such that n(0) = n1 and n(L) = n2

The complicated bit is that x=L/2 there is a further constraint such
that:
a) there is no current flow accross the plane x=L/2 (from either side)
b) there is 'recombination' (i.e destruction of particles) at the plane
L/2 which takes the form (dn/dt) = gamma.na.nb where na and nb are the
concentrations of particles at either side of the plane L/2.

the plane L/2 is thus represented in my finite difference scheme by the
lines

c1.n3 - c1.na - gamma.na.nb = 0
c2.n6 - c2.nb - gamma.na.nb = 0

This makes perfect physical sense in terms what I am modelling, but the
maths of it worries me slightly as I essentially have a discontinuity
at x=L/2. Is SOR even applicable for this task (I have used it
sucessfully to solve the Poisson equation) and if not do you know how
elese I could proceed?

thanks,

Chris




What are n3 and n6?
Are they constants?

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