The　cell　mapping　method　is　a　prominent　one　for　global　analysis　of　nonlinear　dynamical　systems,　with　which　multiple　invariant　sets　can　be　obtained.　However,　it　is　a　continuous　challenge　to　enhance　the　efficiency　of　the　cell　mapping　method,　especially　when　dealing　with　high-dimensional　nonlinear　dynamical　systems.　In　this　paper,　the　subdivision　technique　commonly　used　in　the　cell　mapping　method　is　incorporated　with　an　interpolation　sampling　method,　which　can　further　enhance　the　efficiency　over　the　set-oriented　method　with　subdivision　for　global　attractors　of　nonlinear　dynamical　systems.　In　the　present　method,　a　new　lattice　of　interpolating　nodes　is　adopted　to　fit　into　the　nesting　structures　of　the　subdivided　cells,　portions　of　which　are　sequentially　removed　when　resolution　goes　from　low　to　high.　An　improved　interpolation　method　is　developed　to　obtain　one-step　sample　mappings,　instead　of　integrations　when　error　bounds　are　met,　in　the　process　of　subdivision　iterations.　Furthermore,　a　Hash　table　is　introduced　in　order　to　fast　search　and　locate　the　coordinates　of　cells　that　cover　the　invariant　sets.　Three　examples　of　nonlinear　dynamical　systems　are　presented　to　demonstrate　the　enhancement　in　efficiency　and　effectiveness　of　the　proposed　method,　indicating　that　a　computational　cost　is　one　half　down　to　one　sixth　of　the　previous　methods.　©　2020,　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature.