基于简谐波动模型的法向透射边界及其向任意波动的推广

Normal transmitting boundary based on harmonic wave model and its extension to arbitrary wave

基于外行简谐波动模型、多项式插值理论和具有解析表达式的外插序列,导出了N阶透射边界及其误差项与收敛的充分条件。利用外插序列的时空坐标满足同一直线方程的几何特征,完成了简谐波动N阶透射边界向任意外行波动阶透射边界的推广。依据外插序列的解析表达式,导出了后者误差项的近似表达式和收敛性的充分条件。N阶透射边界的主部与N阶多次透射公式相同,但误差项的表达式不同,精度与收敛性的分析方法与结果也不同。提出了与虚拟透射边界相关的频率放大倍数概念,认为它们是影响虚拟透射边界精度的关键因素。

Based on outgoing harmonic wave model, polynomial interpolation theory and extrapolation sequence with analytical expression, the N - order transmitting boundary and its error - term and the sufficien condition of conver- gence were derived. Using the geometric features that spatiotemporal coordinate of extrapolation sequence satisfies the same linear equation, the extension from N - order transmitting boundary for harmonic waves to that for arbitrary outgoing wave was completed. According to analytical expression of extrapolation sequence, the approximate expres- sion of error-term and the sufficien condition of convergence for the latter were derived. The principal part of N-or- der transmitting boundary is similar to N-order multi-transmitting formula,but the expression of error-term is differ- ent, both analysis method and result of the precision and convergence are different too. New conceptions of frequen- cy amplification were proposed which related to virtual transmitting boundary, and they are considered as the key factors effecting precision of virtual transmitting boundary.