The Impact of AMR in Numerical Astrophysics and Cosmology

I survey the use and impact of adaptive mesh refinement (AMR) simulations in numerical astrophysics and cosmology. Two basic techniques are in use to extend the dynamic range of Eulerian grid simulations in multi-dimensions: cell refinement, and patch refinement, otherwise known as block-structured adaptive mesh refinement (SAMR). In this survey, no attempt is made to assess the relative merits of these two approaches. Rather, the discussion focuses on how AMR is being used and how AMR is making a scientific impact in a diverse set of fields from space physics to the cosmology of the early universe. The increased adoption of AMR techniques in the past decade is driven in part by the public availability of AMR codes and frameworks. I provide a partial list of resources for those interested in learning more about AMR simulations.