Physical-Based Methods for Matrix Compression in Large Array Problems: A Unified View

摘要

In antennas and microwave applications, practical applicability of electromagnetic solvers still remains challenging in a variety of situations of definite industrial or scientific interest; typical large or otherwise complex array antennas, their beam forming networks (BFN), and many instances of MMIC structures are one of the most important such cases. It is to be observed that the scale of the numerical problem may arise from the overall electrical size of the structure under analysis (i.e, in terms of wavelengths) or be determined by the complicacy of its geometrical features. The epitomic example of electrically large structures is the radar cross section computation of large bodies like aircraft; MMIC or other circuits are a typical example of smaller structures with very fine details; full analysis of large array antennas, inter-antenna coupling in large satellites, and the prediction of antenna system performance on complex platforms exhibit a mixture of the two classes of problems. This situation has prompted an active research on ways to reduce the numerical load required to solve large scale problems in terms of numerical complexity and of memory occupation, and this is a very active research field; we will begin with a cursory overview of these efforts. It is to be noted that we are not striving for completeness or citation fairness in describing the existing techniques, but rather we will analyze them in order to set the stage for the present discussion; therefore, only the features that are pertinent to the proposed methods will be mentioned, and only the literature most pertinent to this work is cited; as a consequence, the statement "and references therein" should be applied, to all cited works. To set the terminology, we will call "order of the problem" the number of unknowns required in the standard MoM solution to obtain the desired accuracy in the final outcome of the code (which varies greatly for antenna and scattering problems, the latter requiring a much "softer" description of the near field); in this work we will consider only the methods based on the Integral-Equation (IE)-Method of Moments (MoM) approach.