Fast direct solution of method of moments linear system

Alex Heldring, Juan M. Rius, José Maria Tamayo, Josep Parrón, Eduard Úbeda

Research output: Contribution to journalArticleResearchpeer-review

61 Citations (Scopus)


A novel algorithm, the compressed block decomposition (CBD), is presented for highly accelerated direct (non iterative) method of moments (MoM) solution of electromagnetic scattering and radiation problems. The algorithm is based on a block-wise subdivision of the MoM impedance matrix. Impedance matrix subblocks corresponding to distant subregions of the problem geometry are not calculated directly, but approximated in a compressed form. Subsequently, the matrix is decomposed preserving the compression. Examples are presented of typical problems in the range of 5000 to 70 000 unknowns. The total execution time for the largest problem is about 1 h and 20 min for a single excitation vector. The main strength of the method is for problems with multiple excitation vectors (monostatic RCS computations) due to the negligible extra cost for each new excitation. For radiation and scattering problems in free space, the numerical complexity of the algorithm is shown to be N2 and the storage requirements scale with N3/2. © 2007 IEEE.
Original languageEnglish
Pages (from-to)3220-3228
JournalIEEE Transactions on Antennas and Propagation
Publication statusPublished - 1 Nov 2007


  • Algorithm design and analysis
  • Fast solvers
  • Impedance
  • Impedance matrix compression
  • Linear systems
  • Matrix decomposition
  • Method of moments (MoM)
  • Moment methods
  • Numerical simulation
  • Signal processing algorithms
  • Vectors

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