Research > Solutions of Electromagnetics Problems

Solutions of Electromagnetics Problems Involving Tens of Millions of Unknowns

By achieving the parallelization of MLFMA, which is not trivial at all, we have been able to solve extremely large electromagnetics problems involving tens of millions of unknowns.  Since we are using carefully formulated integral equations, the solutions are not only efficient, but also accurate.  Hence, accurate solutions of previously unsolvable problems are useful both in real-life applications and for benchmarking purposes.  Each solved problem involving tens of millions of unknowns was the largest of its class (hence, a world record) at the time.  Examples of solutions of such extremely large problems are presented here.

Bistatic RCS (in dB) of a sphere of radius 110 wavelengths discretized with 41,883,648 unknowns from 160 degree to 180 degree, where 180 degree corresponds to the forward-scattering direction.

Bistatic RCS (in dBm) of the stealth airborne target Flamme at 16 GHz.  Maximum dimension of the Flamme is 6 m corresponding to 320 wavelengths.  The target is illuminated by a plane wave propagating in the x-y plane at a 30 degree angle from the x axis, as also depicted in the inset. Using wavelength/10 triangulation, the problem is discretized with 24,782,400 unknowns.

For more information:
  • Please see the full article published in the IEEE Transactions on Antennas and Propagation in 2008.

How to cite this paper:
  • Ö. Ergül and L. Gürel, "Efficient parallelization of the multilevel fast multipole algorithm for the solution of large-scale scattering problems," IEEE Trans. Antennas Propagat., vol. 56, no. 8, pp. 2335-2345, Aug. 2008.
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