10 million unknowns: Is it that big?

Sanjay Velamparambil, Weng Cho Chew, Jiming Song

Research output: Contribution to journalArticlepeer-review


At the Center for Computational Electromagnetics at the University of Illinois, we recently solved a very-large-scale electromagnetic scattering problem. We computed the bistatic radar cross-section of a full-size aircraft at 8 GHz, involving the solution of a dense matrix equation with nearly 10.2 million unknowns. We regarded this as the "ultimate test" of a massively parallel implementation of the Multilevel Fast Multipole Algorithm (MLFMA), called ScaleME. In this paper, we narrate the technical difficulties faced and the experience gained from a very informal point of view. We shall describe the various methods developed for surmounting each of the obstacles.

Original languageEnglish (US)
Pages (from-to)43-58
Number of pages16
JournalIEEE Antennas and Propagation Magazine
Issue number2
StatePublished - Apr 2003
Externally publishedYes


  • Electromagnetic scattering
  • Fast multiple method
  • Integral equations
  • Matrix decomposition
  • Matrix inversion
  • Message passing
  • Parallel algorithms
  • Radar cross sections

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Electrical and Electronic Engineering


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