In order to solve these equations we must use AMR. This is because the problem varies over many length scales.
Most difficult part of the solution will be the boundary conditions.
The outer boundary problem will be solved by using a matching condition between a Cauchy(evolution) code, and a characteristic, or perturbation code.
The Cauchy code can ``handle'' the strongly nonlinear regime, and the Characteristic code can ``handle'' only the weakly nonlinear regime. The boundary condition is only known at infinity, thus we need two codes.
