The nested complex source beam method with singular value decomposition

This work present a new aggregation procedure to improve the efficiency of the Nested Complex Source Beam (NCSB) method. The procedure is based on the application of the singular value decomposition (SVD) to the complex source beams (CSBs) aggregation matrices. The matrices, which represent the CSBs relationship between two adjacent levels, are decomposed into new combinations of the original CSBs. By choosing the most relevant singular values and singular vectors, a much more compact representation is obtained to accurately calculate the CSBs interactions. The numerical example is demonstrated to validate the proposed procedure.