Transient implicit wave propagation dynamics with overlapping finite elements

We present novel overlapping finite elements used with the Bathe time integration method to solve transient wave propagation problems. The solution scheme shows two important properties that have been difficult to achieve in the numerical solution of general wave propagations: monotonic convergence of calculated solutions with decreasing time step size and a solution accuracy almost independent of the direction of wave propagation through the mesh. The proposed scheme can be efficiently used with irregular meshes. These properties make the scheme (the combined spatial and temporal discretizations) promising to solve general wave propagation problems in complex geometries involving multiple waves. A dispersion analysis is given and various example problems are solved to illustrate the performance of the solution scheme.