Higher-order Method Of Moments Based On Modified Legendre Polynomial Basis Functions

The RWG basis function which spans on two triangles is associated with a common edge. The MoM using this basis function which requires the length of the mesh as small as 1/10 wavelength will produce a large number of unknowns. Thus, The MoM with the RWG basis function is not suitable for solving the electrically large problems. This thesis presents basis functions which enable large size elements and requires less unkowns than the RWG basis function.This thesis introduces the electric field integral equation and then presents higher order curvilinear geometry modeling and hierarchical arbitrary order functions. These higher order basis functions contain edge basis functions and patch basis functions. The edge basis functions span on two adjacent quadrilaterals which impose normal continuity of current between adjacent elements. The patch basis functions which do not contribute to the normal continuity of the current on the boundary are defined on a single patch. To reduce the condition number of the impedance matrix of MoM with higher order basis functions, modified Legendre polynomials are applied. These baisis functions ensure the continuity without eliminating the orthogonality. As a result of the lower condition number of the impedance matrix of MoM, the algebraic equations with modified Legendre basis functions can be solved iteratively quickly.In the implimentation of higher-order MoM, this thesis uses the concepts of the adjacency matrix and incidence matrix to find the common edges of two adjacent quadrilateral elements. Mathematical expressions of the impedance matrix of any form of higher-order basis functions are presented. The Duffy transform has been applied as an efficient solution of the singular integral problem. Algorithm are validated by examining the current distribution on a plate and the RCS of electromagnetic scattering problems.