A Massively Parallel Multigrid Method with Level Dependent Smoothers for Problems with High Anisotropies

Anisotropic layers, as often seen in biological and geological domains, impose difficulties to several aspects of numerical simulations. In this article we examine how the highly scalable approach to massively parallel geometric multigrid solvers presented in Reiter et al. (Comput Vis Sci 16(4):151–164, 2013) can be extended to problem domains featuring such anisotropies. Considering the real world problem of drug diffusion through the human skin we combine hierarchically distributed multigrids, anisotropic refinement, and level dependent smoothing strategies to create a robust and highly scalable multigrid solver for anisotropic domains.