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This paper, by going one step further in the advancement of the CBFEM approach, presents a memory-efficient technique that derives the CBFs by utilizing a multi-level scheme. This novel approach can be employed in all variety of CBFEM techniques in a similar manner. In the multi-level scheme, the CBFs in each level are progressively combined by grouping a number of sub-domains into larger sub-domains belonging to the higher levels. That is, the CBFs of an arbitrary higher level are determined by employing those of the preceding level. This nested procedure repeatedly utilizes the small-scale CBFEM within a relatively-largescale CBFEM. In this way, a considerable reduction is achieved in memory requirements, especially in large-scale problems. Below the authors first presents a description of the algorithm, and then follow it up with some representative examples to demonstrate the performance of the method in 3D electromagnetic scattering problems.