Remarks On Numerical Simulation Of Near-field Wave Motion

An important research subject is how to analyze the stability of numerical simulation of near-field wave propagation.In this paper, the research work on decoupled numerical simulation of near-field wave propagation in China is reviewed briefly first. Second, a method to determine the stability of transfer matrix , using a sufficient condition based on spectral radius, is discussed. The probably existed problem of that is pointed out. Third, Moshe Goldberg and Eitan Tadmor' s research work on stability theory of difference approximations for mixed initial boundary value problems is introduced in detail, relationship between their work and R. L. Higdon' s work is discussed. We have also given the Lloyd. N. Trefethen' s work a brief introduction. Based on group velocity theory, he gives the GKS perturbation test a clear physical explanation. Fourth the dissipative property of multi-transmitting formula (MTF) implemented by space interpolation is probed. Fifth, the mechanism of oscillation instability of MTF is studied carefully. Form the reflection coefficient presented previously the concept of reflection coefficient in finite domain is first introduced. Sixth, the mechanism of drift instability based on the physical interpretation of GKS stability criterion is remarked. In the end, the drift instability caused by using MTF to simulation the inward propagated wave components.