The method of finite spheres for wave propagation problems

•The development and use of a novel and promising numerical scheme, the method of finite spheres, for the analysis of wave propagations are given.•The solution of two-dimensional linear elastic and visco-elastic waves is considered.•The procedure does not require a mesh and hence avoids element distortions.•The construction of the interpolations is given in which harmonic functions are included to make the method effective for the analysis of wave propagations.•A simple and efficient numerical integration scheme is proposed.

We present in this paper the development and use of a novel and promising numerical scheme, the method of finite spheres, for the analysis of wave propagations. The solution of two-dimensional linear elastic and visco-elastic waves is considered. The procedure does not require a mesh and hence avoids element distortions. We discuss the construction of the interpolations in which harmonic functions are included to make the method effective for the analysis of wave propagations. A simple and efficient numerical integration scheme is proposed and the solution effort is evaluated versus using the standard finite element method. Several numerical examples are used to demonstrate capabilities of the method.