In this study, we develop a novel computational framework called Overlapping Spectral Element Method (OSEM). The OSEM is based on the overlapping finite element method and spectral element method with higher-order interpolation functions, which can be effective for the analysis of structural dynamics and wave propagation problems. In this method, there are three types of spectral elements: regular, coupling, and overlapping. The mass matrices of overlapping and coupling elements are not diagonal, whereas the mass matrices of regular spectral elements are inherently diagonal. Hence, using the elements employed in the mesh, an explicit–implicit or implicit time integration method can be utilized for the time integration. The OSEM includes the advantages of both overlapping finite element and spectral element methods to provide higher accuracy and less element geometric distortion sensitivity than the traditional spectral element method in modeling complex domains. Finally, we demonstrate the merits of using the proposed solution procedure in comparison to using the traditional spectral element method in the solution of several numerical examples.
