Asynchronous space–time algorithm based on a domain decomposition method for structural dynamics problems on non-matching meshes

Large-scale practical engineering problems featuring localized phenomena often benefit from local control of mesh and time resolutions to efficiently capture the spatial and temporal scales of interest. To this end, we propose an asynchronous space–time algorithm based on a domain decomposition method for structural dynamics problems on non-matching meshes. The three-field algorithm is based on the dual-primal like domain decomposition approach utilizing the localized Lagrange multipliers along the space and time common-refinement-based interface. The proposed algorithm is parallel in nature and well suited for a heterogeneous computing environment. Moreover, two-levels of parallelism are embedded in this novel scheme. For linear dynamical problems, the algorithm is unconditionally stable, shows an optimal order of convergence with respect to space and time discretizations as well as ensures conservation of mass, momentum and energy across the non-matching grid interfaces. The method of manufactured solutions is used to verify the implementation, and an engineering application is considered, where a sandwich plate is impacted by a projectile.