Application of a Hierarchical SVD/ACA Compression Technique to Near-Field Calculations of Monopole Antennas

This paper describes the concept of hierarchical matrices and the application to near-field calculations of voltage or power driven antennas. The hierarchical matrix structure is based upon a binary partition of the structure to be analyzed, where blocks of the matrix can be represented as full matrices or R(k)-matrices, the latter yielding a data reduced representation of the initial block. It has been found that application of only the ACA (adaptive cross-approximation) matrix reduction technique gave bad results in many practical 3D cases and failed to predict the physical current distribution. Way out of this dilemma is to combine ACA with SVD (singular value decomposition), yielding reliable results again. The new compression scheme turns out to be efficient and stable and will be described in detail. By means of examples the validity of the approach is demonstrated, where especially near-field investigations are carried out.