Hello,
I'm working on a 1D problem with a PDE defined on a whole interval mesh but with a constraint (enforced through Lagrange multipliers) on a subdomain of the said interval mesh.
Basically, it is similar to any mesh that would have an obstacle inside the main domain that constrain the range of solutions.
Here is the code I use to define the mesh and subdomains:
from dolfin import *
mesh = UnitIntervalMesh(50)
subdomains = MeshFunction('size_t',mesh,0)
class domain_1(SubDomain):
def inside(self, x, on_boundary):
return between(x[0],(0.3,0.6))
subdomains.set_all(0)
subdomain1 = domain_1()
subdomain1.mark(subdomains,1)
dx=Measure('dx')[subdomains]
ds=Measure('ds')[subdomains]
And the representation of subdomains to be clearer:
What I'd like to know is, in this case, what exactly does ds(0) means? I assume ds(1) represents the interior facets of subdomain 1, so the points x=0.3 and x=0.6, then ds(0) would be points x=0.0 and x=1.0?
The thing is that the Lagrange multiplier has to be defined over the whole domain and I have to specify the boundary conditions on the borders of the constrained subdomain but I don't know if I use the ds(i) measure correctly..
Any help will be much appreciated! Best regards.
