Hi Garth, On 01/09/2014 10:49 AM, Garth N. Wells wrote: > 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? >> 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. > Yes. Look at the demo > > demo/documented/neumann-poisson > > Garth
Thanks for the quick reply! So if I understand correctly, I don't need to do anything special for the boundary conditions because Dolfin assumes Neumann by default, and Neumann conditions are only reflected in L. However, even after going through the example, I'm not sure how I can tell FEniCS to use only trial functions satisfying Laplace's equation. In the example, the constraint on the test functions seems to fix just the constant offset. It's not clear to me to extend this to something more complicated, where the constraint itself takes the form of a PDE. Do you think you could explain in a bit more detail? Best, Nikolaus -- Nikolaus Rath, Ph.D. Senior Scientist Tri Alpha Energy, Inc. +1 949 830 2117 ext 211 _______________________________________________ fenics mailing list [email protected] http://fenicsproject.org/mailman/listinfo/fenics
