On 2014-01-09 18:40, Nikolaus Rath wrote:
Hello,
I would like to solve the following equation (which does not directly
come from a PDE):
\int dV f(x) * \partial_r g(x) = \int dA u(x) * \partial_n g(x)
f(x) is known, u(x) is unknown, and the equation should hold for any
g(x) that satisfy Laplace's equation.
In other words, I'm looking for a weight function u(x), such that the
surface integral of the normal derivative of any g(x) (weighted by u)
gives the same result as the volume integral of the radial derivative
of
g(x) (weighted by the known function f(x)).
Is it possible to do this with FEniCS?
Yes. Look at the demo
demo/documented/neumann-poisson
Garth
It seems that the equation itself is easy to express in UFL, but I am
not sure how do deal with the fact that there are no boundary
conditions, and that any trial function g(x) needs to satisfy Laplace's
equation.
Best,
Nikolaus
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