Dispersion-reducing finite elements for transient acoustics

This paper focuses on increasing the accuracy of low-order four-node quadrilateral finite elements for the transient analysis of wave propagation. Modified integration rules, originally proposed for time-harmonic problems, provide the basis for the proposed technique. The modified integration rules shift the integration points to locations away from the conventional Gauss or Gauss-Lobatto integration points with the goal of reducing the discretization errors, specifically the dispersion error. Presented here is an extension of the idea to time-dependent analysis using implicit as well as explicit time-stepping schemes. The locations of the stiffness integration points remain unchanged from those in time-harmonic case. On the other hand, the locations of the integration points for the mass matrix depend on the time-stepping scheme and the step size. Furthermore, the central difference method needs to be modified from its conventional form to facilitate fully explicit computation. The superior performance of the proposed algorithms is illustrated with the help of several numerical examples. © 2005 Acoustical Society of America. DOI: 10.1121/1.2011149