Multi-scale Problem And Multi-component Problem Based On Integral Equation Methods

Multi-scale problems and multi-component problems exist in many practicalengineering applications, for example, the electromagnetic analysis of dielectricradomes with frequency selective surfaces. However, multilayer fast multi-polealgorithm (MLFMA) suffers from inefficiency due to the the dense discretization for thefine features when applied for the multi-scale problems. This is because the cube atlowest level may still hold a huge amount of unknowns since its electrical size could notbe smaller than a threshold value, typically0.20.3wavelength. The accurate analysisand fast solution of composite metallic and thin dielectric sheet structures is also alwaysa challenge in CEM discipline at the same time. The accelerated Cartesian expansion(ACE) algorithm is proposed in this paper and we combine it with MLFMA for theanalysis of multi-scale problems both efficiently and accurately. In the end, the hybridalgorithm is used as a fast solution to multilayer thin dielectric sheet (TDS)approximation model consisting of thin dielectric sheet and metallic structures with finefeatures.First, the integral equation and its numerical solution-method of moment (MoM) isintroduced. The basis functions widely used and the calculation of the elements ofimpedance matrix is studied. The basic principles and numerical implementation ofMLFMA as a fast solution to integral equation is demonstrated and the disadvantage ofthe algorithm when applied for multi-scale problems is shown.Then, we propose ACE algorithm and combine it with MLFMA. The principlesand numerical implementation is discussed in detail and the elements of impedancematrix are expressed in the form of Cartesian tensors. Then the hybrid algorithmincluding ACE and MLFMA based on adaptive data structure is developed andaccelerates the matrix-vector multiplication in iterative solution when applied formulti-scale problems.Finally, the TDS approximation model is introduced. Since this model is thesimplification of volume integral equation model and the volume integral is replaced bysurface integral, we could reduce the number of unknowns significantly. Then we employ the hybrid algorithm to analyze the TDS model consisting of dielectric andmetallic structures with fine features both efficiently and accurately.