A higher order parallelized multilevel fast multipole algorithm for 3-D scattering

Kalyan C. Donepudi, Jian Ming Jin, Sanjay Velamparambil, Jiming Song, Weng Cho Chew

Research output: Contribution to journalArticlepeer-review


A higher order multilevel fast multipole algorithm (MLFMA) is presented for solving integral equations of electromagnetic wave scattering by three-dimensional (3-D) conducting objects. This method employs higher order parametric elements to provide accurate modeling of the scatterer's geometry and higher order interpolatory vector basis functions for an accurate representation of the electric current density on the scatterer's surface. This higher order scheme leads to a significant reduction in the mesh density, thus the number of unknowns, without compromising the accuracy of geometry modeling. It is applied to the electric field integral equation (EFIE), the magnetic field integral equation (MFIE), and the combined field integral equation (CFIE), using Galerkin's testing approach. The resultant numerical system of equations is then solved using the MLFMA. Appropriate preconditioning techniques are employed to speedup the MLFMA solution. The proposed method is further implemented on distributed-memory parallel computers to harness the maximum power from presently available machines. Numerical examples are given to demonstrate the accuracy and efficiency of the method as well as the convergence of the higher order scheme.

Original languageEnglish (US)
Pages (from-to)1069-1078
Number of pages10
JournalIEEE Transactions on Antennas and Propagation
Issue number7
StatePublished - Jul 2001


  • Electromagnetic scattering
  • Fast solvers
  • Parallel processing

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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