Updating vector fields in subdomains

Question

Hi list,

I've got a problem at hand that is related to subdomains. Consider the following simplified problem:

• We want to solve a time-dependent ODE on a mesh $\Omega = \Omega_1 \cup \Omega_2$ that is subdivided into two sub-domains.
• The solution is a (vector) field $\vec{v}$ over the whole domain $\Omega$.
• The right-hand side of the ODE depends on the whole vector field $\vec{v}$
• In $\Omega_1$ we fix the vector field to some user-given value, while in $\Omega_2$ the vector field can vary with time.
• The goal is to advance the whole vector field from time $t$ to $t+h$ with updates only acting on $\Omega_2$.
• At each time step, we also want access to the full vector field.

I guess that one can more-or-less easily achieve this but I haven't been able yet to figure out the correct FEniCS way of doing so ...

Answer 1

One way could be to apply a DirichletBC to subdomain 1, see e.g. [1,2,3] , constraining the velocity field to its prescribed user-defined value.

[1] https://www.mail-archive.com/fenics-support@fenicsproject.org/msg00258.html
[2] https://fenicsproject.org/qa/8780/what-is-the-best-way-to-set-a-subdomain-to-a-given-value?show=8780#q8780
[3] https://fenicsproject.org/qa/10593/mixed-space-formulation-on-distinct-domains?show=10593#q10593

Comments

This looks feasible. I'll give it a try... Thank you!