thx. well f(x,y) is an unknown as well as f_3D but maybe an iteration would work if one is not using a direct solver? so maybe? any suggestions? ________________________________________ From: firedrake-bounces@imperial.ac.uk <firedrake-bounces@imperial.ac.uk> on behalf of Lawrence Mitchell <lawrence.mitchell@imperial.ac.uk> Sent: Monday, April 25, 2016 11:53 AM To: firedrake@imperial.ac.uk Subject: Re: [firedrake] use of BCs for interior nodes On 25/04/16 11:30, Onno Bokhove wrote:
Are these implicit bc's? they are unknowns but that is something else, isn't?
the key issue is not solving these equations but extending a surface 2D function vertically.
so if this does not work, then it goes back to the query I had a week or so ago for which you guys said that a hack could work;l i.e.: (i) iiint f(x,y) * h(x,y,z) dx dy dz = iint f(x,y) [int h(x,y,z) dz ] dx dy
as that is the alternative.
otherwise, we need f(x,y) as on the RHS of the above specified everywhere in the 3D domain.
of course, the domain is extruded in the z-direction in regular fashion.
(ii) the trick Floriane is now trying is solving
d_zz f_3D(x,y,z) = 0 with f_3d is f(x,y) at the top and bottom as part of a larger system of water wave equations.
So is the problem that you want to solve d_zz f_3D(x, y, z) = 0 with strong dirichlet conditions at top and bottom set by f(x, y). In which case, the previous suggestion of copying from top to bottom works. So if your process is something like: solve for f(x, y) construct f_3D Use f_3D in a system X. Then that's fine. Presumably solving X you might construct a new solution for f, but you're happy using the old value in f_3D (which enters through the right hand side)? Lawrence