Performance of an implicit time integration scheme in the analysis of wave propagations

In earlier work an effective implicit time integration scheme was proposed for the finite element solution of nonlinear dynamic problems [1] and [2]. The method, referred to as the Bathe method, was shown to possess unusual stability and accuracy characteristics for the solution of problems in linear and nonlinear structural dynamics [1], [2] and [3]. In this paper we study the dispersion properties of the method, in comparison to those of the widely used Newmark trapezoidal rule, and show that the desired characteristics of the Bathe method for structural dynamics are also seen, and are very important, in the solution of wave propagation problems. A dispersion analysis is given and problems are solved to illustrate the capabilities of the scheme for the solution of wave propagation problems.

► The solution of wave propagation problems is considered.
► The implicit Newmark trapezoidal rule and Bathe methods are used.
► The methods are analysed for dispersion errors.
► The Bathe method is found to be effective for the solution of wave propagation problems.