Coupling Ritz Method and Triangular Quadrature Rule for Moving Mass Problem

Abstract

In this paper, a mixed method that combines the Ritz method and the triangular quadrature rule (TQR) is presented for solving time-dependent problems. In this study, the Ritz method is first used to discretize the spatial partial derivatives. The TQR is then employed to analogize the temporal derivatives. The resulting algebraic formulation is a triangular matrix equation, which reduces to the solution of a system of algebraic equations of the size of the problem for each time step. This requires less computational effort compared to the differential quadrature method (DQM) where a larger system of the size of the problem should be solved within each time element. The mixed formulation combines the simplicity of the Ritz method and accuracy and computational efficiency of the TQR. The stability property and computational efficiency of the scheme are discussed in detail. Numerical results show that the proposed mixed methodology can be used as an efficient tool for handling the time-dependent problems.