Efficient simulation of waves in heterogeneous domains using the scaled boundary finite element method

Abstract

AbstractSimulation of wave propagation phenomena is very challenging due to the restrictions placed on the spatial as well as on the temporal discretization. Image‐based domain discretization using hierarchical meshes (2D polygonal elements) in conjunction with the scaled boundary finite element method provides an efficient numerical simulation tool. In this setting, the computational effort is reduced as only a limited number of unique cell patterns are formed. This is beneficial while computing element matrices in the preprocessing stage. When solving the dynamic system, the advantages of similar elements can only be fully exploited for the explicit time‐stepping schemes in connection with mass lumping when the domain is discretized using low‐order elements (p ≤ 2). On the other hand, the time step size may be limited by the stability criterion. Moreover, high‐order elements require fewer degrees of freedom. Hence for a specific application, it is not straightforward to predict superiority of one time‐stepping scheme over the other. A comparative study of implicit and explicit time‐stepping schemes is presented using an artificial two‐material model.