Static validation test: Radial profile of the gravitational field along (θ, φ) = (π/2, 0). The radius is in log scale. The grid configuration and boundary conditions are the same as our fiducial run, but we halved the resolution on each axis, uniformely for each patch. The density distribution is a uniform off-centered sphere of radius 1000, located at (r, θ, φ) = (3000, π/2, 0). We set ${\rho }_0=\frac{3}{4\pi }$ and G ≡ 1 and the quantities are displayed in code units. The blue line is the theoretical profile, red dots are the computed data.