> In the first layer where I want to compute u_1 I have a homogenous mixed
> boundary condition, after that I go to the next layer then in order to
> ensure the continuity of spreading the light between a miss-matched
> interfaces we will face the the following two boundary conditions
>
> u_2 = \frac{n_1}{n_2}u_1 .............(1)
> \frac{\ ptl u_2 }{\ptl z}=\frac{D_1}{D_2}\frac{\ ptl u_1 }{\ptl z}
> ..............(2)
>
> So we computed u_1 in the first layer and after that have it like a vector
> valued to compute u_2, then I think there is no problem.
You assume that you can compute u1 in the first layer without knowing u2. But
that isn't true. The interface conditions between layers you have say that a
certain fraction of the light intensity from layer 1 crosses into layer 2, but
it also implies that another fraction of the light intensity in layer 2
crosses into layer 1. In other words, you can only solve for layer 1 when you
know what the light intensity in layer 2 is, but of course also the other way
around -- the problem is coupled.
Best
W.
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Wolfgang Bangerth email: [email protected]
www: http://www.math.tamu.edu/~bangerth/
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