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Topic: measured boundary conditions with pde toolbox
Replies: 17   Last Post: Apr 8, 2014 6:00 AM

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Bruno Luong

Posts: 8,563
Registered: 7/26/08
Re: measured boundary conditions with pde toolbox
Posted: Aug 6, 2009 1:27 AM
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"Doug " <dhk@umd.edu> wrote in message <h5daso$lqr$1@fred.mathworks.com>...
> Hmmm, I haven't heard of Dirac-Neumann boundary conditions. In this problem I want to specify the normal derivative of the scalar field at each node on the boundary.
>
> Anyway, that's not the sticky part--what I'm unsure about is how to specify boundary conditions from measured data, instead of specifying them as a constant or an analytic function of coordinates.
>
> --Doug


You can't. Physically, it does not make sense to measure the flux at one point locally. You need to know the flux on the boundary *entirely*. You might assume that your flux is constant or linear by edge, but you measure it at the nodes, but you cannot assume a partial flux. Take a semaphore, you can't estimate accurately the water going out a pond by measuring the water speed at one single point (or many few of them).

Constant Neumann du/dn = g on gamma (the boundary)
<=> specify integral (du/dn.f) dx := integral g.f dx, for all f

Dirac Neuman du/dn = g delta (xi)
<=> specify integral (du/dn.f) dx := g.f(x), for all f

However you won't be able to define the above integral if you only know du/dn at the nodes (you will need to know du/dn in the edge entirely)

Bruno



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