Stability and accuracy improvement for explicit formulation of time domain acoustic problems

Due to the “wave velocity error” between the discretized model and continuum systems, the accuracy of numerical results using standard finite element method (FEM) in time domain acoustic problems is unsatisfactory with increasing frequency. Such wave velocity error is strongly related to the balance between the “stiffness” and “mass” of discretized systems. By adjusting the location of integration point of mass matrix, the redistribution of the mass is able to “tune” the balance between the stiffness and mass. Thus, the wave velocity error can be minimized in time domain acoustic problems with a balance system. On the other hand, it is found that the stability of discretized model of time domain acoustic problems can be improved by the softened stiffness. Furthermore, it is found that the balance between the smoothed stiffness and mass can also be achieved with the tuning of integration point r in the mass matrix.