On mass lumping and explicit dynamics in the scaled boundary finite element method

We present, for the first time, the application of explicit time-stepping schemes within the context of the scaled boundary finite element method (SBFEM). To this end, we discuss in detail how and under which circumstances diagonal mass matrices can be obtained. In addition, we propose an approach to improving the interpolation accuracy of quadratic scaled boundaryshape functions. In essence, our results show that mass lumping can be achieved without loss of accuracy if linear or quadratic node-based shape functions are deployed for the interpolation on the subdomain boundaries. This finding also applies to non-convex elements, which allow coarse discretizations - and, hence, comparably large time steps - in problems involving singularities. We discuss the application to polygonal and severely distorted meshes. Numerical examples include problems from the fields of acoustics, elasticity, and thermal diffusion. (C) 2020 Elsevier B.V. All rights reserved.