  We present a simple and effective multigrid-based Poisson solver of
second-order accuracy in both gravitational potential and forces in terms of
the one, two and infinity norms. The method is especially suitable for
numerical simulations using nested mesh refinement. The Poisson equation is
solved from coarse to fine levels using a one-way interface scheme. We
introduce anti-symmetrically linear interpolation for evaluating the boundary
conditions across the multigrid hierarchy. The spurious forces commonly
observed at the interfaces between refinement levels are effectively
suppressed. We validate the method using two- and three-dimensional
density-force pairs that are sufficiently smooth for probing the order of
accuracy.
