A multilevel non-uniform grid (MLNG) algorithm is used for acceleration of iterative integral equation based analysis of scattering from arbitrary shaped large bodies. The acceleration is achieved by replacing the matrix-vector products performed by an iterative method of moments (MoM) solver by an equivalent fast field evaluation via the MLNG algorithm. The MLNG field evaluation scheme is based on recursive domain decomposition, field sampling over coarse non-uniform grids, and interpolation. Inherently geometrically adaptive, it has been proved to lower 3D field evaluation computational complexity and memory requirements from O(N2) (N being the number of unknowns) to O(N log N). Applied for acceleration of an MoM iterative solver for scattering problems, the MLNG is not affecting the number of iterations needed for convergence for quasi-planar, elongated, and full 3D problems.