时域有限差分并行算法中的吸收边界研究

Study on Absorbing boundary condition in parallel FDTD algorithm

针对并行FDTD中以二阶Mur、单轴各向异性介质完全匹配层(UPML)和卷积形式完全匹配层(CPML)为吸收边界的并行化处理方法进行论述。用金属球的远区散射计算,并与Mie级数解对比,验证了并行计算中三种吸收边界的吸收效果。最后给出UPML吸收边界FDTD计算内存估计公式,并以电大尺寸目标卫星模型为例对并行性能进行了测试。由于并行中通信时间影响并行加速比和效率,UPML和CPML吸收边界的相邻子域数据通信方式与FDTD迭代式相同,而Mur吸收边界的相邻子域间数据通信方式与FDTD完全不同,它的并行性能要低于前两者。电大尺寸卫星目标模型的多机并行计算测试结果表明,UPML和CPML并行FDTD计算的并行加速比及其效率整体上高于Mur,其中CPML吸收条件下的效率达到90%以上。

The parallel processing method taking the second-order Mur, the uniaxial anisotropic perfectly matched layer （UPML） and the convolutional perfectly matched layer （CPML） as the absorbing boundary conditions （ABC） respectively in finite difference are analyzed. The efficiency obtained from these ABCs is verified through computing the scattered field by a metallic sphere, and a comparison with the Mie＇s Series solution is made. The memory estimate formula of a three-dimensional （3D） parallel FDTD algorithm using UPML ABC is also provided. The parallel performance is tested by taking the model of a targe-size target satellit as an example. The data communication between sub-domains in UPML and CPML is of the same manner as in the FDTD iterative scheme. However, the way of data communication between sub-domains in Mur＇s ABC is quite different from the way in FDTD that increases the complexity of programming. The communication among sub-domains in parallel computing influences strongly the parallel performance, hence that to Mur＇s ABC is inferior to UPML and CPML. The calculated result to large-size satellite model by multiple computers also shows the speedup factor and efficiency for using UPML and CPML are superior to using Mur＇s ABC. Furthermore, the efficiencies for CPML are all above 90%.