Different mesh cell sizes at different subdomains

Question

Hey,

In this simple example, I have a rectangular domain with inside a circular subdomain. When solving Poisson's equation inside my domain, I'm particularly interested in the solution in the circular subdomain, while the rest of my domain is of less interest. So I want different mesh cell sizes; a dense mesh inside the circle, a coarser mesh outside. The very simple code to plot the equal-meshed domain looks like:

domain=Rectangle(-10,-10,10,10)
domain.set_subdomain(1,Circle(0,0,4))
mesh=Mesh(domain,20)
plot(mesh,interactive=True)

So you can adjust the whole mesh spacing with the second argument of Mesh(domain,20). How to refine the mesh inside the circular subdomain, without changing the outer mesh?

Thanks for any help,

Adriaan

Answer 1

You could continue with something like

cc = CellFunction("bool", mesh, False)
circle = AutoSubDomain(lambda x: sqrt(x[0]*x[0]+x[1]*x[1]) < 4+1e-8)
circle.mark(cc, True)
mesh = refine(mesh, cc)

Comments

This works fine, thanks!
Is it also possible to manually adjust the mesh sizes? When you create a circular mesh like

CircleMesh(Point(0.0),4,3.0)

the mesh spacing is regulated by the third parameter (3.0 here). Is it also possible to do something like this for the mesh refinement in the circular subdomain?