A Novel Broadband Multilevel Fast Multipole Algorithm With Incomplete-Leaf Tree Structures for Multiscale Electromagnetic Problems

Creative Commons License

Takrimi M., Ergul O., Erturk V. B.

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, vol.64, no.6, pp.2445-2456, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 64 Issue: 6
  • Publication Date: 2016
  • Doi Number: 10.1109/tap.2016.2552545
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2445-2456
  • Keywords: Broadband solvers, incomplete leaf (IL), low-frequency breakdown, multilevel fast multipole algorithm (MLFMA), multiscale problems, HELMHOLTZ-EQUATION, SCATTERING
  • Middle East Technical University Affiliated: Yes


An efficient and versatile broadband multilevel fast multipole algorithm (MLFMA), which is capable of handling large multiscale electromagnetic problems with a wide dynamic range of mesh sizes, is presented. By invoking a novel concept of incomplete-leaf tree structures, where only the overcrowded boxes are divided into smaller ones for a given population threshold, versatility of using variable-sized boxes is achieved. Consequently, for geometries containing highly overmeshed local regions, the proposed method is always more efficient than the conventional MLFMA for the same accuracy, while it is always more accurate if the efficiency is comparable. Furthermore, in such a population-based clustering scenario, the error is controllable regardless of the number of levels. Several canonical examples are provided to demonstrate the superior efficiency and accuracy of the proposed algorithm in comparison with the conventional MLFMA.