Evolutions in 3D numerical relativity using fixed mesh refinement

We present results of 3D numerical simulations using a finite difference code featuring fixed mesh refinement (FMR), in which a subset of the computational domain is refined in space and time. We apply this code to a series of test cases including a robust stability test, a nonlinear gauge wave and an excised Schwarzschild black hole in an evolving gauge. We find that the mesh refinement results are comparable in accuracy, stability and convergence to unigrid simulations with the same effective resolution. At the same time, the use of FMR reduces the computational resources needed to obtain a given accuracy. Particular care must be taken at the interfaces between coarse and fine grids to avoid a loss of convergence at high resolutions. This FMR system, "Carpet", is a driver module in the freely available Cactus computational infrastructure, and is able to endow existing Cactus simulation modules ("thorns") with FMR with little or no extra effort