So I am pretty excited about the capability in FreeFEM to solve problems with large contrast in the material properties through the FFDM/HPDDM solver (https://doc.freefem.org/documentation/ffddm/tutorial.html) So far in the literature I have only seen examples for elasticity or other elliptic operator. I am wondering if these methods can be applied to the Stokes-Brinkman problem with also large contrast in the Brinkman properties or if this is still an open question on the research of DDM.
Yes, it can be applied.
See one of the many examples:
You may find additional details there as well: Introduction to FreeFEM with an emphasis on parallel computing.