Pade 型双向抛物方程及其在室内电波传播问题中的应用研究

摘要

针对室内垂直墙面、家具等对电磁波后向反射较大的问题，提出了 Pade 型双向抛物方程，在增大抛物方程计算角度的同时提高了室内场计算的精度。利用 Crank-Nicolson 有限差分法推导了 Pade 型双向抛物方程的离散差分格式，同时，通过对室内天花板和地板采用阻抗边界条件，导出了上下边界场满足的有限差分格式，与射线跟踪法的对比验证了边界处理的正确性。采用双向抛物方程仿真了包含家具的单层单建筑物存在时室内电磁波的传播特性，结果表明，双向抛物方程的仿真结果是可靠的，其符合现实物理规律，最后基于该双向抛物方程模型模拟和分析了存在二栋双层建筑物时室内的电磁波分布特性。%In order to increase the calculating angle of parabolic equation and improve the calculation accuracy when solving the problem of multiple reflection field,such as indoor propagation environments,the Pade two-way parabolic equation is presented. Its discrete difference format is deduced via the Crank-Nicolson finite difference method.Besides,the finite difference scheme of field on the upper and lower boundaries is educed by using the impedance boundary condition to the indoor ceiling and floor,whose correctness is verified compared with ray tracing method.The characteristics of indoor radio wave propagation in a single-storey building including one furniture are simulated by two-way parabolic equation.The results show that the two-way parabolic equation is reliable and agreeable to the physical laws.Finally,the two-dimensional parabolic equation model is applied to computing the in-door distribution characteristics of electromagnetic waves,when two double-floor buildings exist.