Research On Hybrid Fast Algorithm For Multiscale Electromagnetic Problems

With the development of information science and technology, more and more complex elec-tromagnetic field problems continue to emerge. In particular, how to quickly and efficiently solve the multiscale electromagnetic scattering problems presents a great challenge for compu-tational electromagnetics. Many previous fast methods used to analyze electromagnetic scatter-ing from electrically large complex objects encounter different degrees of difficulties in dealing with such problems. This thesis focuses on the research of integral equation-based hybrid fast algorithm for multiscale problems, and the obtained results and innovations are summarized as follows:1. The MLFMA equipped with a hybrid tree structure is proposed for solving multiscale electromagnetic scattering problems. Compared with the MLFMA with a single oct-tree structure, the MLFMA equipped with a hybrid tree structure can significantly reduce the memory requirement for the near-field matrix in dealing with multiscale problems.2. The MLFMA with the assistance of the FFT-based method is proposed for solving mul-tiscale electromagnetic scattering problems. In this method, the MLFMA bears the main part of the computation at the macro level, while some FFT-based method is responsi-ble for the computation on the subregion with finer meshes, avoiding the inherent sub-wavelength breakdown of the MLFMA, and hence, the solution of the entire model has a higher numerical accuracy and efficiency (storage efficiency and computational effi-ciency).3. The FFT-based algorithm with the near-matrix compression is proposed for solving mul-tiscale electromagnetic scattering problems. A hierarchical grouping of all RWG ba-sis functions is introduced into the framework of the FFT-based algorithm, resulting in a block-sparse structure of the near-matrix such that the low-rank matrix compression technology can applied to the near-matrix. Compared with the traditional FFT-based algorithm, the FFT-based algorithm with the near-matrix compression can effectively re-duce memory requirement of the near-matrix without increasing time spent of the matrix-vector product.4. The FG-FFT algorithm (or the FGG-FG-FFT algorithm) combined with the interpolation technique of the near-field matrix (FG-FFT with the Near-field Matrix Interpolation) is used to fast and accurately analyze the wideband electromagnetic scattering characteristic of electrically large objects. The proposed algorithm has no the sub-wavelength break-down, and is not sensitive to both the grid spacing and the expansion order. Therefore, it can realize the fast and accurate calculation of frequency sweep.