Singular Value Decomposition of the Radiation Operator—Application to Model-Order and Far-Field Reduction

2008 ◽  
Vol 56 (6) ◽  
pp. 1605-1615 ◽  
Author(s):  
Bruno Stupfel ◽  
Yoann Morel
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Far Field ◽  
Model Order ◽  
Value Decomposition

A singular value decomposition based approach for far-field reconstruction from irregularly spaced planar wide-mesh scanning data

2007 ◽  
Vol 49 (7) ◽  
pp. 1768-1772 ◽  
Author(s):  
F. D'Agostino ◽  
F. Ferrara ◽  
C. Gennarelli ◽  
R. Guerriero ◽  
M. Migliozzi ◽  
...  
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Far Field ◽  
Field Reconstruction ◽  
Value Decomposition

scholarly journals A Truncated Singular Value Decomposition Enhanced Nested Complex Source Beam Method

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Lianning Song ◽  
Zaiping Nie
Keyword(s):  
Singular Value Decomposition ◽  
Radiation Power ◽  
Singular Values ◽  
Beam Width ◽  
Singular Value ◽  
Far Field ◽  
Truncated Singular Value Decomposition ◽  
Complex Source ◽  
Equivalent Sources ◽  
Value Decomposition

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.

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