The Method of Moments in Electromagnetics, 3rd Edition

Chapter 10

Multi-Level Adaptive Cross Approximation

In Chapter 9, basis functions were clustered into spatially localized, roughly same-sized groups via the K-means algorithm, imposing a block structure on the MoM matrix. It was then shown that the off-diagonal blocks in the system matrix, as well as the corresponding off-diagonal LU matrix blocks, can be compressed via the ACA+QR/SVD technique (Section 9.2.2). As K-means is not a hierarchical algorithm, a single set of basis function groups is created. Thus, we refer to this approach as the single-level ACA, or simply the ACA.

It was pointed out in [1] that the degrees of freedom (DoF) remain asymptotically constant when size of the source and testing groups are inversely varied. This concept ...