Efficient iterative solution of electromagnetic scattering using adaptive cross approximation enhanced characteristic basis function method

Abstract

A new hybrid adaptive cross approximation-characteristic basis function method (ACA-CBFM) is proposed to efficiently solve the electromagnetic scattering problems. In the conventional ACA-CBFM, the ACA is only applied to speed up the construction of the reduced matrix that is directly solved and stored. However, with the increase of the size of the targets under analysis, the reduced matrix will become so large that it is difficult to directly solve and store. In this study, the reduced matrix is further compressed by the adaptive cross approximation-singular value decomposition (ACA-SVD) and solved by an iterative method, which leads to reduced storage and accelerated matrix vector product. Furthermore, the ACA-SVD is adapted to efficiently generate the characteristic basis functions (CBFs), which reduces both the time of generating initial CBFs and the SVD time of initial CBFs. Numerical results about the electromagnetic scattering from perfect electric conducting targets are given to demonstrate the merits of the proposed methods.

Fast direct solution of characteristic basis function method using ACA-based LU decomposition

“…(5) can be efficiently calculated by many fast techniques [10,11,12]. Finally, after generating the reduced matrix equation, the coefficients of the CBFs can be directly solved by using the LU decomposition to the reduced matrix Z R .…”

“…The main computational cost of the CBFM consists of two parts: (1) the generation of the reduced matrix; (2) the LU solution of the reduced matrix equation. The cost of the reduced matrix generation have been successfully alleviated by many techniques [9,10,11,12,13]. Theses methods greatly enhance the efficiency of the reduced matrix filling.…”

Multilevel Fast Adaptive Cross-Approximation Algorithm With Characteristic Basis Functions

“…The details of generating the CBFs are omitted, which can be found in [18], [25], and [26]. Assuming that the CBFs have been generated, the interactions Z R i,j between the CBFs in a far-block pair (i, j) at level l can be expressed as…”

“…Nevertheless, in the hybrid ACA-CBFM, the reduced matrix is not compressed, which is directly stored and solved by a conventional direct approach. In [26] and [29], the authors have shown the compressibility of the reduced submatrix Z R i,j between well-separated high-level blocks, and use the ACA [11] or the ACA-SVD [17] to compress Z R i,j after it is generated. However, the generation of Z R i,j is very time consuming for large blocks.…”

Accelerated characteristic basis functions generation of large block with Sherman‐Morrison‐Woodbury algorithm and characteristic basis function method

“…In recent years, several schemes have been proposed to accelerate the CBFs generation 8‐16 . One of them is to bypass the solution of dense matrices with a high‐frequency asymptotic technique, such as physical optics, 8,9 and with a multilevel approach by partitioning the spectrum of the incident plane waves 10 or partitioning the large blocks 11 .…”