Hello Ahmad,
thanks for the explanation. I think you can almost drop condition (1)
completely. Let me explain why: For problems with pure Neumann boundary
conditions one usually has to constrain one boundary dof to some
"practical" value, say 0, to obtain a unique solution. This is the case
because, if one only prescribes derivatives of a function, the function
can be shifted arbitrarily and still fulfills all conditions. For your
problem this means that you can impose Neumann boundary conditions (2)
as usual, but you have to pick out one boundary dof and impose condition
(1) by inserting the right-hand side value \frac{n_1}{n_2} u_1 in the
constraint matrix for this degree of freedom. Then the Neumann boundary
conditions should take care that also on all other points on the
boundary the solution has the correct values. Probably the best choice
to impose the constraint is a degree of freedom which is assigned to a
vertex, because you can obtain its physical location easily.
Hope this helps,
Markus
Am 16.08.11 11:25, schrieb Ahmad Al Nabulsi:
Hi Markus,
the problem is diffusion of the light in multi-layers translucent
materials.
so between the layers I mean after getting the computations in the
first layer for example, we need a continuty condition so the next
conditions are needed
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)
where n_1, n_2 are the refractive index of the first and the second
layery resp.
D_1 ,D_2 are the diffusion constant of the first and the
second layery resp.
the second boundary condition refers to that the flux on the boundary
from the first side (which one can comute it depending on the
computations in the first layers after postprocessing the solution in
the first layer) is equal to the flux on the same boundary but in the
other side.
I do not know whether one can neglict it from the computation .....
best regards,
ahmad
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