What is the advantage of handling domains with different materials using subdomains?

Question

Dear all,

So I have been looking at the tutorial about using subdomains and there must be something I do not understand because I have always been doing as follows:

def isInRegion1(x):
    return   x[1]<0.5e-2 

class MyCrossSection(Expression):
    def eval(self, value, x):
        if  isInRegion1(x):
            value[0] = sigma_t_1
        else:
            value[0] = sigma_t_2

    def value_shape(self):
        return (1,)

Sigma_t = MyCrossSection()
...
a += (Sigma_t[0]+1/(c*dt))*psi*v*dx  # some component of the bilinear form

Which seems easier to me to use than subdomains.

So I probably don't get the full potential of using subdomains. Are there cases in which subdomains could help do something that the method above could not?

Thanks a lot!
Vincent

Answer 1

Hi,

I personally prefer the subdomains approach, as it allows me to write one version of the weak form and specify material regions programmatically (by subclassing SubDomain and manually marking the subdomains MeshFunction as described in the tutorial) in simple cases, while use GMSH for more complicated material regions (to be honest, I use GMSH even for simpler regions as I like to see what is marked before I run the calculation).

So I typically create a mesh and specify physical regions in GMSH, run the .msh file through dolfin_convert and just use

subdomains = MeshFunction("size_t", mesh, "mesh_physical_regions.xml")

with the generated physical regions file (analogous approach can be used also for boundaries).

Comments

I think I better understand why using subdomains is preferable, thanks a lot!

Answer 2

Hi,

I find it convenient to use subdomains when I am dealing with materials with rough, irregular interfaces. It also means I can write a script that robustly imports different meshes from external specialist mesh programs like GMSH.

Comments

Thanks for the answer! :)

What confuses me is that in both cases you need to define a function to explicit what is in a given region and what is not (isInRegion1(x) in the example above and inside(self, x, on_boundary) if using subdomains)

So could you explain to me why the second approach is more robust?

I am asking this because I precisely imported a mesh from GMSH and the solver takes forever (compared to if I use a similar mesh using RectangleMesh) so I am wondering if it is because I should use subdomains or not

Thanks for the help!

Answer 3

Suppose you have a circular subdomain. Of course you can treat it as above. But after obtaining the solution, suppose you want to evaluate an integral on the subdomain, you can compute it very easily as Fdx(i) where i is ith subdomain .

You might be able to do this your own way, but I think it will be painful .

Comments

That's indeed a good reason to use subdomains, thanks!