I've got a sphere in a cube with each having different materials and
each being governed by different equations. At interface between the
sphere and the cube, there's a zero neumann boundary condition from the
sphere while there's a dircihlet condition for the cube's inner surface
(with u_cube_inner_surface = u_sphere_surface).
My plan is to have two triangulations: one for the sphere and one for
the cube and then manually set the vertices on the cube's inner surface
to the solution values at the corresponding vertices on the sphere surface.
a) Is this the best way to do it?
Yes, I think that makes sense.
b) If it is, assuming I load two different meshes (one for the sphere
and the other for the cube), what can I do if the vertices at the
interface do not line up?
That's difficult. Then the solutions on the two sides of the interface
will not be exactly equal (they can't, in general, unless the solution
is constant). You can enforce continuity weakly, for example using the
mortar method.
c) On the other hand, If I load a single mesh with the cube and sphere
merged, can I split the mesh into two sub-meshes and work on each
individually?
Yes, see step-46.
Best
W.
--
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Wolfgang Bangerth email: [email protected]
www: http://www.math.tamu.edu/~bangerth/
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