Abstract: We present an out-of-core multigrid for solving the Poisson equation defined over gigantic meshes. This enables gradient-domain operations on out-of-core meshes with irregular connectivity. Taking a streaming mesh and boundary constraints as input, our solver builds a multigrid hierarchy and refines the multigrid solution progressively by performing all operations as streaming computations. A set of rules are carefully designed to make neighboring multigrid nodes perform tasks cooperatively and efficiently. With a sublinear memory growth with respect to the number of mesh vertices, our approach handles meshes with 14M vertices using merely 84MB of memory, while an equivalent in-core multigrid implementation fails to fit into 2GB memory space.