  Typical areas of application of explicit dynamics are impact, crash test, and
most importantly, wave propagation simulations. Due to the numerically highly
demanding nature of these problems, efficient automatic mesh generators and
transient solvers are required. To this end, a parallel explicit solver
exploiting the advantages of balanced octree meshes is introduced. To avoid the
hanging nodes problem encountered in standard finite element analysis (FEA),
the scaled boundary finite element method (SBFEM) is deployed as a spatial
discretization scheme. Consequently, arbitrarily shaped star-convex polyhedral
elements are straightforwardly generated. Considering the scaling and
transformation of octree cells, the stiffness and mass matrices of a limited
number of unique cell patterns are pre-computed. A recently proposed mass
lumping technique is extended to 3D yielding a well-conditioned diagonal mass
matrix. This enables us to leverage the advantages of explicit time integrator,
i.e., it is possible to efficiently compute the nodal displacements without the
need for solving a system of linear equations. We implement the proposed scheme
together with a central difference method (CDM) in a distributed computing
environment. The performance of our parallel explicit solver is evaluated by
means of several numerical benchmark examples, including complex geometries and
various practical applications. A significant speedup is observed for these
examples with up to one billion of degrees of freedom and running on up to
16,384 computing cores.
