Transient implicit wave propagation dynamics with the method of finite spheres

• The method of finite spheres enriched for transient wave propagation problems.
• Implicit time integration, the Bathe method.
• Monotonic convergence of calculated solutions with smaller time step sizes.
• Dispersion analysis of solution schemes.
• Numerical solutions to demonstrate the important attributes of the solution schemes.

In the paper by Ham et al. (2014), the method of finite spheres enriched for transient wave propagation problems was used and a monotonic convergence of the calculated solutions with decreasing time step size was seen. This is an important property for practical analyses and different from what is seen in traditional finite element solutions. In this paper we explicitly show and study this characteristic through a dispersion analysis of the solutions calculated by the method of finite spheres using an implicit time integration method, the Bathe method. Another important property identified is that in uniform spatial discretizations for the problems solved, the calculated solution accuracy is almost independent of the solution direction considered. Numerical solutions of some wave propagation problems are given to demonstrate these attributes and show that with the schemes discussed very accurate response predictions can be obtained.