On Mon, Nov 2, 2015 at 12:45 PM, tschroeder <tschroe...@daad-alumni.de> wrote:
> Hi there, > > > I am trying to solve the Laplace equation for the magnetic potential in a > 3D domain (a cube). > > It's free space and does not contain any sources. > > I do have magnetometer readings for discrete points on the volume's > surface (Neumann-type problem). > OK... I don't really know much about magnetometers, but if you are solving the Laplace equation with Neumann BCs, there are several examples (e.g. systems_of_equations_ex1) in the library that demonstrate how to impose Dirichlet BCs using a penalty approach, which you could follow (sans the penalty) for imposing Neumann BCs. My questions are: > > 1) I assume that I don't need to bother with providing a function for the > exact solution. Correct ? > Yes, unless you want to estimate the error, or verify your code is working with manufactured solutions, etc... 2) The magnetometer sensitivity axis was not aligned with the surface > vectors. Can I define Neumann boundary conditions with arbitrary (but > known) directions in Libmesh? > Not really sure what you mean. The BC in the weak formulation of Laplace's equation involves the gradient of the unknown dotted with the outward unit normal. I don't know of any alternative formulations... can you somehow estimate the normal component of the measured data? 3) Any other suggestions for where to get started? > Start by modifying one of the existing examples to do what you want, you can move this to a stand-alone application later fairly easily. -- John ------------------------------------------------------------------------------ _______________________________________________ Libmesh-users mailing list Libmesh-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/libmesh-users
