Anisotropic High-Contrast Problems

In this paper, we study robust two-level domain decomposition preconditioners for 10 highly anisotropic multiscale problems. We present a construction of coarse spaces 11 that emploies initial multiscale basis functions and discuss techniques to achieve 12 smaller dimensional coarse spaces without sacrificing the robustness of the precon13 ditioner. We also present numerical results and consider possible extensions of these 14 approaches where the dimension of the coarse space can be reduced further. 15