Abstract
This work presents a novel matrix compression algorithm to improve the computational efficiency of the nested complex source beam (NCSB) method. The algorithm is based on the application of the truncated singular value decomposition (TSVD) to the multilevel aggregation, translation, and disaggregation operations in NCSB. In our implementation, the aggregation/disaggregation matrices are solved by the truncated far-field matching, which is based on the directional far-field radiation property of the complex source beams (CSBs). Furthermore, the translation matrices are obtained according to the beam width of CSBs. Due to the high directivity of the radiation patterns of CSBs, all the far-field related interaction matrices are low-ranked. Therefore, TSVD can be employed and a new set of equivalent sources can be constructed by a linear combination of the original CSBs. It is proved that the radiation power of the new sources is proportional to the square of the corresponding singular values. This provides a theoretical guideline to drop the insignificant singular vectors in the calculation. In doing so, the efficiency of the original NCSB method can be much improved while a reasonably good accuracy is maintained. Several numerical tests are conducted to validate the proposed method.
Highlights
Integral equation (IE) method has been intensively studied in the analysis of electromagnetic (EM) radiation and scattering in recent years
The higher order basis functions (HOBF) [6], phase extracted basis functions (PE) [7, 8], characteristic basis function (CBF) [9, 10], or body of revolution (BoR) [11] MoM are proposed to reduce the number of unknowns in a given problem
The balance between accuracy and computational efficiency can be controlled by adjusting the truncation threshold
Summary
Integral equation (IE) method has been intensively studied in the analysis of electromagnetic (EM) radiation and scattering in recent years. In order to conduct large-scale simulations, a variety of numerical techniques have been developed based on MoM These techniques are carried out efficiently either by reduction of the far-field interaction exploiting the physical or mathematical properties of the IE or by using well-designed basis/test functions to reduce the total number of unknowns. A complex source beammethod of moments (CSB-MoM) is recently proposed to accelerate the far-field interactions of MoM [12]. A nested complex source beam (NCSB) method is proposed by utilizing an equivalent relationship between adjacent levels [18] This relationship is built by treating CSBs in the child group as new sources and applying the far-field matching to get their CSB expansions in the parent group. Thereby, the proposed method leads to a significant improvement of the computational efficiency and provides a flexible compromise between accuracy and computational cost
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