A New Sparse Technique for Singular Integral Equations in Electromagnetics

摘要

Recently, several fast computational methods based on directly thinning the matrix of method of moment (MoM), such as impedance matrix localization (IML) (1), wavelet expansions (2), and reduced expansion and field testing (REFT)(3), have been introduced. In this paper, a simple matrix composition technique, based on the concept of measured equation of incariance (MEI) (4), is proposed to numerically thin the matrix from singular integral equations, such as methods of moment (MoM). This technique is referred to as matrix decomposition by the MEI concept (MDMEI). The MEI mthod was initially applied in finite-difference (FD) or finite-element (FE) methods to terminate the truncated boundary as close as possible to the object surface, and has been recently developed to the onj-surface MEI (OSMEI) method (5)-(6), in which the FD or FE meshes are avoided. Although OSMEI generates highly sparse matrix (6) on the same mesh as MoM, the matrices of OSMEI are distinguished from that of MoM. This is because OSMEI describes a local relation between the scattered electric fields and the scattered magnetic fields rather than a relation between the scattered fields and surface current densities. Hence OSMEI is not direct for those who are familiar with the MoM. Since sparse matrices have many advanages for saving storage and ocmputing time for large-size problems, many efforts have been done to thin the full matrix generated by the MoM, such as the IML (1) adn REFT (3) mentioned above. In order to generate the sparse matrix with as a little additional work on any of a variety of existent MoM programs, the MDMEI method is proposed in this paper. The MoM matrices for a variety of problems. such as the electrostatic problems, wire antennas, and 2-and 3-D conducting object scattering can be easily thinned by MDMEI.