Fast Analysis for Complicated Electromagnetic Problems and the Software Implementation
|School||Nanjing University of Technology and Engineering|
|Course||Electromagnetic Field and Microwave Technology|
|Keywords||method of moment CG-FFT multilevel fast multipole method preconditioning techniques sparse-matrix/canonical grid method finite element-boundary integral method higher order vector basis function|
The electromagnetic scattering and radiation of 3D complex targets have attractedmuch more attention in engineering applications. Recently, intensive investigations havebeen done to find fast and accurate numerical methods to solve such problems. Themethod of moment (MoM) has been widely used to analysis the scattering and radiationproblems. However, the conventional MoM requires a discretization of typically ten perwavelength, which generates a large number of unknowns in handling large-scaleproblems for a desired accuracy. There are three ways to attack such a trouble in MoM.The first way is to develop some fast algorithms, for example, the conjugate gradient fastFourier transform (CG-FFT) and the multilevel fast multipole method (MLFMM), toaccelerate the matrix vector multiply. The second way is to find some new basis functions,including high order basis functions. The last way is to study the efficient iterativespeeding algorithms to reduce the condition number of the operator equations. Thisdissertation is focus on the later two approaches and their combination with the MLFMMand CG-FFT. The main contribution include:1. Detailed work has been done for the numerical implementation of MoM to solvepractical problems. We have studied the extraction of the singularities and nearsingularities in the elements of impedance matrix with different base functionsincluding RWG and curve RWG base functions and analyzed the antenna todemonstration the accuracy of the method.2. The inner-outer Flexible Generalized Minimum Residual algorithm (FGMRES) andloose GMRES algorithm combined with FFT technique are used to accelerate theiteration when analyzing the arbitrary dielectric body with large permittivity.Furthermore, the FGMRES-FFT algorithm is applied for the analysis of scattering andradiation by the cavity-backed patch ahtennas and arrays based on the finite element-boundary integral (FE-BI) method. As a result, significant convergence improvementis achieved.3. The sparse-matrix/canonical grid (SMCG) method is studied. The generalized product-type method based on Bi-CG (GPBi-CG) combined with the SMCG method toanalyze scattering of randomly positioned and oriented dielectric spheroids. As aconsequence, good convergence is achieved.4. The higher order interpolatory vector basis function combined with MLFMM is applied to analysis the electromagnetic scattering and radiation of electrical-largetargets. The near-field preconditioning technique is proposed to accelerate theconvergence of the MLFMM with the high order interpolatory vector basis fuction.5. A new kind of higher order hierarchical basis functions is proposed to analysis theelectromagnetic scattering and radiation of electrical-large targets. The new multi-gridpreconditioning technique is proposed to accelerate the iteration of the MLFMM withthe higher order hierarchical basis functions.6. A robust, efficient and practical software is developed to analyze the electromagneticscattering and radiation of electrical-large targets. The software is much accurate andhas been validated using analytical solutions and experimental data for typical PECtargets.