Space–time collocation meshfree method for modeling 3D wave propagation problems

In this work, a novel local space–time domain collocation technique—space–time boundary moving least squares (BMLS–ST) method, which has been proposed for modeling 3D propagation problems in the 4D spatiotemporal domain. The transient wave equations are approximated by four 1D boundary shape functions on the X-, Y-, Z-, and T-axis within the BMLS–ST implementation. Specifically, due to the local approximation feature of the moving least square in 1D shape functions, the BMLS–ST results in a large-scale sparse linear system that is easy to store and solve. In addition, based on the boundary moving least square 3D spatial approximation, we introduce the Newmark implicit integration scheme to develop the boundary moving least square Newmark approximation formula (BMLS–NM). The identical spatial discretization scheme is adopted in the two methods proposed here, with different temporal approximations. The numerical results demonstrate that the BMLS–ST is of a high order of accuracy, easy to carry out, and utilizes large time steps for modeling transient 3D wave propagation problems. This work provides a numerical basis for further research on the dynamic analysis of discontinuous the arch dam model.