Study On Bilinear Higher Order Laminar Vector Basis Function In Integral Equation Method

The method of moments has been widely used to analyze the EM scattering from objects because of its high accuracy. This thesis studied on the linear-linear basis functions, which aimed to improve the precision of the integral equation methods.Firstly, this thesis introduced the definition of the linear-linear basis functions and the basic theory of the MoM. The linear-linear basis functions are divided into divergence conformal ones and the curl conformal ones. The second chapter introduced the divergence- and curl-conforming linear-linear basis functions which are defined on plane triangular elements. Both of them were discussed in details.Secondly, the divergence-conforming linear-linear basis functions were employed to expand the induced surface current on the scattering objects. The further research shows that the accuracy of the linear-linear basis functions is very high with larger mesh size when compared with the RWG basis functions. The multilevel fast multipole algorithm was applied to accelerate the matrix vector productors.Thirdly, the linear-linear basis functions combined with higher order hierarchical vector basis functions was introduced. The divergence-conforming and curl-conforming linear-linear higher order hierarchical vector basis functions were applied to both the CFIE and the MFIE. The accuracy can be guaranteed by the proposed basis functions with larger meshes when compared with the higher order hierarchical RWG basis functions.Finally, the divergence-conforming linear-linear basis functions were used in PMCHW integral equations to analyze the EM scattering from dielectric objects.