基于Daubechies尺度函数的共形MRTD方法研究及其电磁散射应用

为了降低Yee氏蛙跳式网格划分的台阶误差，该文对3维曲面导体目标进行精确电磁建模，将时域多分辨(MRTD)算法与共形时域有限差分(CFDTD)算法结合，提出一种新的基于Daubechies尺度函数的共形时域多分辨(CMRTD)方法。该文提出将基于Daubechies尺度函数的MRTD迭代公式分解为若干传统FDTD迭代公式的线性组合，然后对最里面回路上的FDTD分解式运用局部共形技术，再将各个分解式进行线性组合，从而得到CMRTD结果。仿真结果表明，CMRTD方法既保持了MRTD方法节省计算资源、计算效率高等优点，同时明显提高了计算的精度。

Research and Application to Electromagnetic Scattering of Conformal MRTD Method Based on Daubechies Scaling Functions

In order to reduce the staircasing error of Yee’s leap-frog meshing and accurately model three- dimensional curved conducting objects, a new Conformal MultiResolution Time-Domain (CMRTD) method based on Daubechies’ scaling functions is proposed by combining the MultiResolution Time-Domain (MRTD) algorithm with the Conformal Finite-Difference Time-Domain (CFDTD) algorithm. This paper puts forward to decompose the MRTD update equation based on Daubechies’ scaling functions into a linear combination of several conventional Finite-Difference Time-Domain (FDTD) update equations. Then locally conformal technology is applied to the FDTD decomposition equation on the innermost loop. Finally, all decomposition equations are linearly combined into the CMRTD result. Simulation results show that CMRTD can not only preserve MRTD’s advantages of saving of computational resources and high computational efficiency, but also enhance computational precision obviously.