Multiscale Domain Decomposition Preconditioners for Anisotropic High-Contrast Problems

In this paper, we study robust two-level domain decomposition preconditioners for highly anisotropic multiscale problems. We give a construction of coarse spaces that employ initial multiscale basis functions and discuss techniques to achieve smaller dimensional coarse spaces without sacrificing the robustness of the preconditioner. We also present numerical results and discuss possible extensions of these approaches where the dimension of the coarse space can be reduced.