Many physical problems have variations in scale.
When solving these problems numerically, high grid resolution is needed to adequately solve the equations. Limitations on computational resources often force a compromise on grid resolution, resulting in under-resolution of the problem. Solutions to Poisson's equation, for example, can exhibit this type of variation, due to local concentration of charges or boundary conditions. Unfortunately, local refinement introduces several added issues like matching of the solution at grid interfaces. We have developed an AMR Poisson solver code which solves Poisson's equation using multigrid relaxation.