Explicit　time　integration　methods　are　an　integral　part　of　solving　structural　dynamics　problems　such　as　the　propagation　of　elastic　and　acoustic　waves,　impact　scenarios　including　crash　tests　and　many　more.　One　common　limitation　of　this　class　of　time　integrators　is,　however,　their　conditional　stability,　meaning　that　highly　distorted,　small,　or　stiff　finite　elements　typically　govern　the　critical　time　step　size.　That　is　to　say,　even　a　small　number　of　such　elements　will　result　in　a　significantly　decrease　of　the　feasible　time　step,　which　in　turn　drastically　increases　the　computational　costs　of　solving　the　semi-discrete　equations　of　motion.　This　is　especially　true　for　non-uniform　and　unstructured　meshes.　Therefore,　an　asynchronous　explicit　solver　in　parallel　is　proposed　in　this　article.　The　idea　is　to　assign　different　time　step　sizes　to　different　parts　of　the　mesh,　such　that　the　overall　computational　effort　is　minimized.　To　improve　the　performance　of　the　proposed　solver,　it　is　combined　with　a　sophisticated　octree　meshing　framework,　where　the　balanced　octrees　are　used,　meaning　that　the　ratio　of　the　element　sizes　of　adjacent　elements　cannot　exceed　a　value　of　two.　Thus,　the　critical　time　step　of　each　element　can　be　estimated　straightforwardly.　To　avoid　issues　with　hanging　nodes,　a　special　polyhedral　element　formulation,　the　scaled　boundary　finite　element　method,　is　employed.　Since　there　are　only　a　limited　number　of　cell　patterns　in　a　balanced　octree,　the　stiffness　and　mass　matrices　are　pre-computed,　significantly　reducing　the　computational　cost.　Moreover,　exploiting　an　element-by-element　technique,　the　assembly　of　global　stiffness　matrices　can　be　avoided.　The　main　advantage　of　the　described　methodology　is　that　the　asynchronous　explicit　solver　can　be　easily　implemented　in　a　high-performance　computing　environment.　By　means　of　several　numerical　examples,　the　accuracy　and　efficiency　of　the　proposed　method　are　demonstrated,　as　well　as　its　versatility　in　handling　complex　engineering　problems.　(c)　2022　Elsevier　B.V.　All　rights　reserved.