近场波动数值模拟稳定性问题分析

Stability analysis for numerical simulation of near-field wave motion

本文利用分析一维双曲型偏微分方程初边值问题数值稳定性的GKS定理的物理解释和推广 ,以出平面波动为例 ,分析了集中质量显式有限元方法及中心有限差分方法分别与多次透射公式简单结合构成的封闭数值求解系统的稳定性 ,并用数值试验进行了验证。旨在从概念上说明讨论人工边界稳定性时 ,必须与计算区域内的具体算法结合分析才有意义 ,单纯地说人工边界在数值计算中稳定或不稳定是不正确的。

Based on the interpretation and generalization of GKS theorem of initial and boundary problem numerical stability for 1-D hyperbolic partial differential equation, taking plane SH wave as an example, stability of two closed-numeric-solution systems was analyzed in the paper. One system is simply composed of multi-transmitting formula and lumped mass explicit finite-element method; the other is composed of multi-transmitting formula and central finite difference method. The results were tested with numerical experiments too.Our purpose is to explain that it is necessary to link with the arithmetic used in calculating area to say stability or unstability when discussing stability problem of artificial boundary.