Research On Key Techniques Of High-order Numerical Method

The researchs on EM scattering from the targets with complex geometrical shape,material composition and extremely-electrically-large size have important significancefor the application of target identification, target stealth and microwave imaging. Thefast algorithm in the field of CEM, MLFMA for example, is able to lower down thecomputational complexity and storage complexity for numerical solution to O(Nlog(N)),but wich is still related to the number of unknowns N. All the factors, application ofhigher frequency, larger medium electromagnetic parameters and huge physicaldimension, lead to enormous number of unknowns. Even with fast algorithms, therequirements of memory and computing time are sometimes far beyond affordablerange. For the purpose of simplifying the computation model and based on a profoundunderstanding of the physical laws which surface induced current should comply with, anew set of basis function, based on triangular patch, with excellent capacity to describephase changing and standing wave distribution of the induced surface current isdesigned in this paper. And then combined with the MLFMA, the problem ofelectromagnetic scattering from metal, dielectric and metal-dielectric composite targetsare solved efficiently.Specifically, based on the curvilinear RWG basis function and a type of orthogonalscalar hierarchical polynomials, this dissertation construct a set of divergence-conforming hierarchical high-order vector (HHOV) basis functions firstly. And thenapply them to the MLFMA framework to enhance the analytical ablity of EM scatteringfrom various targets. Then the triangular-based hierarchical basis function and anothersets of large-patch basis function, namely phase extracted basis function (PE) andquadrangular-based hierarchical basis function, are studied and compared deeply. Afterdoing this, we are familiar with the advantage and disadvantage of the basis functionsand all the technical details, which lay a foundation for this dissertation to propose thenew travelling standing wave basis function (TSW).Then, combined with PE basis function and triangular-based hierarchical basisfunction, a new set of high-order vector bases, named TSW bases, are proposed in this paper. Such bases have an excellent ability to describe phase changing and standingwave distribution of the surface current even defined on larger patches. Compared withthe low order method, the number of unknowns can be lowered down1~2order(s); onthe other hand, the basis order can be reduced1~2order(s) compared with thehierarchical basis functions. At the same time, EM scattering from two kinds of typicalmetal targets, i.e. nonsmooth convex target and strong coupling target, are mainlyanalysised by using the TSW bases.Finally, in combination with surface integral equation (SIE) method and the newtype basis function proposed in this dissertation, the EM scattering characteristics ofdielectric and metal-dielectric composite targets are analysed. Among them, the well-conditioned SIE, namely combined field integral equation (CFIE) and electric-magneticcurrent CFIE (JMCFIE), are used to solve the induced surface electric current and theequivalent surface electric-magnetic current. For the new basis functions sill have thehierarchical characteristic, the p-adaption is preliminarily analyzed. Taking advange ofthe divergence-conforming HHOV basis function and the TSW basis function, a highefficient numerical codes, HHOV/TSW-CFIE-JMCFIE-MLFMA, is developed toanalyze EM scattering characteristics of several classic targets, such as dielectricradome (including metal antenna), coated targets and so on.