A New Sub-entire-domain Basis Function Method

Sub-Entire-Domain(SED)basis function method is a Macro Basis Function(MBF)method based on Moment of Method(Mo M),and have been proved efficient for solving large-scale finite periodic structures with electrically isolated elements.However,the finite periodic structures are connected in most instances for practical engineering application,the computational accuracy of traditional SED basis function method would be decreased with the narrowing of gap distance between cell elements.Thus,in this paper,with the concept of degree of freedoms(DOFs)of solution spectrum,the new SED basis function method is proposed based on the traditional SED basis function method.The main contents and research works in this paper includes the following parts,1.The traditional SED basis function method is derived in detail to deal with the electromagnetic scattering and radiation problem,including the selection of the low level basis function as RWG,the SED based MBF such as Accurate SED(ASED)basis function and Simplified SED(SSED),the excitation source in scattering and radiation problem and the computation of the far field.The phenomenon for the decreasing computational accuracy in the traditional SED basis function method with the narrowing gap distance is further illustrated.2.In order to handle the problem of stronger coupling between cell elements with the narrowing gap distance,the multiple plane waves(MPWs)were introduced to enlarge the degree of solution spectrum,and the new ASED basis function method is derived.Similar with the traditional ASED basis function method,the procedure for the new ASED basis function method can also be divided into two parts,the problem for the several physical cells in the plane wave incidence and the problem for the periodic structure represented by the ASED basis functions.3.Furthermore,owing to the introduction of the MPWs,there exists the redundancy in the new ASED basis function.To improve the efficiency of the new ASED basis function method,the singular value decomposition(SVD)is applied,and a set of orthometric ASED basis functions are obtained.Thus,the number of unknowns of the second problem in the new ASED basis function method have been reduced significantly and the LU decomposition can be used directly to solve the matrix.The several numerical results are given to prove the accuracy and the efficiency of the new ASED basis function with SVD in the computation of the periodic structures with arbitrary gap distance.4.The Discontinuous Galerkin based on Integration Equation(IEDG)is further combined in the new ASED basis function,which improved the flexibility of the boundary handling and extended the scope of application for the periodic structure with the fine object.