Development of special finite elements for two-dimensional elastic wave problems

In order to model wave problems using the finite element method, it is usual to discretise the domain such that there are about ten nodal points per wavelength. However, such a procedure is computationally expensive and impractical if the wavelength is short and/or the computational domain is large. The aim of the proposed research is to develop finite elements for elastic wave problems capable of containing many wavelengths per nodal spacing rather than many elements per wavelength. This will be achieved by applying the plane wave basis decomposition to the elastic wave equation. These elements will allow us to relax the traditional requirement of around ten nodal points per wavelength and therefore solve elastic wave problems without refining the mesh of the computational domain at each frequency.Compared with conventional finite element meshes, the proposed finite elements are capable of reducing the total number of variables needed to solve a problem by up to 90%. This will allow fast and accurate solutions of elastic wave problems, and will lead to huge savings in terms of computer simulation time and memory.