Almost all questions I've seen so far deal with unit squares or cubes and explicitly use a priori knowledge of the facet locations to implement periodic boundary conditions. I'd like to know if one can come up with a more generalized version of a PeriodicBC class.
More specifically: Given a D-dimensional Mesh mesh and a MeshFunction facets (that obviously marks the (D-1)-dimensional facets), I would like to write a PeriodicBC to map facet1 to facet2, but I'm somewhat lost in the specs/doc to find out the bits and pieces I need for that. Any help would be appreciated!
class PeriodicBC(SubDomain):
def __init__(self, facet1, facet2):
self.facet1 = facet1
self.facet2 = facet2
# Check that `x` is element of boundary `facet1`.
def inside(self, x, on_boundary):
# ?
# Map point `y` on `facet2` onto point `x` on `facet1`.
# This is probably much more complicated and may as
# well involve facet normal vectors.
def map(self, x, y):
y[0] = ?
y[1] = ?
# y[2] = ? # if 3D mesh
