Unaffordable　computational　cost　and　memory　storage　induced　by　the　curse　of　dimensionality　has　become　the　bottleneck　of　numerical　methods　in　different　fields.　In　the　global　analysis　of　nonlinear　dynamical　systems,　the　capability　of　numerical　methods,　like　cell　mapping　methods,　are　mostly　feasible　only　to　a　system　dimension　less　than　four.　Although　cell　mappings　are　naturally　parallelizable　that　may　be　used　to　greatly　enhance　the　computational　efficiency,　it　is　still　not　enough　to　release　the　computational　burden　on　a　higher-dimensional　system　of　greater　than　seven,　not　to　mention　the　memory　in　dealing　with　millions　of　billion　cells.　In　this　paper,　the　subdomain　synthesis　method,　which　partitions　the　chosen　region　in　state　space　into　subdomains　suitable　for　operating　in　a　computational　unit　and　then　synthetizes　the　so-called　virtual　invariant　sets　to　get　the　underlying　global　invariant　sets,　is　promoted　to　be　parallelizable　on　the　subdomains　so　as　to　build　a　two-layer　massively　parallel　architecture　in　both　cell　and　subdomain　levels.　The　proposed　approach　can　be　implemented　by　GPU　Cluster　that　can　maximize　the　powerful　computation　capability　of　hardwares.　Examples　with　global　invariant　sets　in　very　fine　distances　of　a　Jerk　system　and　in　bifurcations　of　a　twelve-dimensional　nonsmooth　rotor　system　are　presented　for　the　first　time　to　demonstrate　then　the　feasibility　of　the　proposed　approach.　©　2022　World　Scientific　Publishing　Company.