Testing a New Mesh Refinement Code in the Evolution of a Spherically Symmetric Klein–gordon Field

Numerical evolution of the spherically symmetric, massive Klein–Gordon field is presented using a new adaptive mesh refinement (AMR) code with fourth order discretization in space and time, along with compactification in space. The system is non-interacting, thus the initial disturbance is entirely radiated away. The main aim is to simulate its propagation until it vanishes near [Formula: see text]. By numerical investigations of the violation of the energy balance relations, the space–time boundaries of "well-behaving" regions are determined for different values of the AMR parameters. An important result is that mesh refinement maintains precision in the central region for a longer time even if the mesh is only refined outside of this region. The speed of the algorithm was also tested; in the case of ten refinement levels the algorithm was two orders of magnitude faster than the extrapolated time of the corresponding unigrid run.