Study Of Parallel FDTD Algorithm And EM Scattering In Layered Half-space

This dissertation lays a strong emphasis on the essential elements of a parallel algorithm for the Finite Difference Time Domain (FDTD) method based on MPI platform and the key techniques of plane wave injection in layered half-space to EM scattering analysis.Based on the MPI (Message Passing Interface) library, an MPI Cartesian three-dimensional (3D) topology is used. A 3D Cartesian topology is defined and the FDTD computation domain is divided into some subspaces using a spatial decomposition of the regular grid structure. Then the fields inside each sub-domain are computed on an individual processor with a small amount of data being communicated from neighborhood sub-domain. For each field component, all the sub-domains send data in one direction sub-domain and receive data from opposite direction simultaneously. The transmission and reception can therefore be done with only one instruction, such as the procedure of SendRecv(), which optimizes the communication order and avoids the deadlock caused by this order. The inter-process communications are optimized by the use of derived data types, which group the data even when their memory addresses are not continuous, then the discontinuous data can be transmitted only once. Thus the optimized 3D parallel FDTD program can be resulted.This dissertation discusses with emphasis on the parallel processing method to the absorbing boundary condition (ABC) including the second-order Mur`s absorbing condition, the uniaxial anisotropic perfectly matched layer (UPML) and convolutional perfectly matched layer (CPML). The load balance and absorbing performance of these ABCs are also analyzed. The CPML ABC has the advantages of high performance in parallel computation, readily programming and high-absorbing as well. The efficiency up to 90% calculated by parallel FDTD with CPML for large-size satellite is reached. It applies not only to the isotropic but also to the dispersive and the anisotropic media. The numerical results to several dispersive models validate our parallel algorithm. The radar cross sections (RCS) to the targets of complex shape, such as helicopter and compound wing, and the targets of complex material, such as the compound isotropic media wing and compound anisotropic media sphere are analyzed by using the parallel FDTD method.In application of FDTD to the scattering analysis of object embedded in layered half-space, especially to the dispersive and lossy media, the injection of incident electromagnetic plane wave becomes complicated, because the traditional method in free space is not applicable. The plane wave to 3D FDTD in layered half-space is in fact a 2D problem. To solve this problem, the hybrid scheme is presented: the incident wave along side TF-SF boundaries are governed by the 1D modified Maxwell`s equations (1D MME); the incident wave on the upper TF-SF located in free space is in fact a duplication of the waveform at the cross points of TF-SF boundary with a proper time delay; the lower TF-SF boundary can also be treated by the same way as the upper, if the lowest layer medium is non-dispersive and lossless. However, the lowest layer medium with dispersive and lossy medium is of interested, and then we extend the side TF-SF downwards into CPML, which makes sure that the downward traveling wave is absorbed at lower media by the ABC. The presented hybrid scheme withΠ-shape being unclosed, it is unnecessary to determine the incidence wave along the lower TF-SF as it does in the traditional closed scheme.To inject the plane wave into layer half-space in 2D FDTD, the formulations to 1D MME for TM and TE mode are developed. Furthermore, the discretization to TE mode is more difficult. Then an auxiliary magnetic variable is used, the 1D modified FDTD (MFDTD) to TE mode without any approximation and a three-step averaging technique in discretization to ensure convergence and improve precision is proposed. Considering three classes of dispersive material of Debye, Lorentz and Drude media, a uniform auxiliary update equation is derived.Based on 3D CPML ABC, the CPML ABCs applicable to 2D and 1D case for TM and TE modes are derived, respectively. Then, these ABCs are applied to truncating FDTD domain in dispersive and lossy media successfully.The Courant stability criterion in 1D-MFDTD is analyzed for different incident angles. The result shows that 1D-MFDTD is of instability while the incident angle is greater than 60°, because the phase velocity becomes larger along the y-direction . The feasibility of the algorithm is validated by using several dispersive layered half-space models from different aspects. The results by 1D MFDTD are in good agreement with Fourier transform method. The plane wave is introduced in 3D FDTD using the result of 2D FDTD computation, 2D and 3D FDTD simulations produce perfectly plane wave consisting of incident, reflected and transmitted wave. The parallel algorithm is also proposed and implemented to deal with the large-size target scattering in layered half-space. The numerical results show that the parallel and serial algorithms can obtain the same result. The significance and valuable application of this study are proved by several practical models. Finally, the model of land mine detection indicates the high performance to the parallel FDTD algorithm in layered half-space.