Electrical and Computer Engineering
Department of Electrical and Computer EngineeringUniversity of Illinois Urbana-Champaign



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FMA Library--A MOM/Integral Equation Broadband Acceleration Software

Register for a copy of FMALib1.0 by clicking here.

FMALib is a library code for broadband acceleration of the matrix-vector product of integral equation solvers such as the method of moments. It uses a mixed-form fast multipole algorithm, and hence, it is valid from static physics (circuit physics) to wave physics problems. It has been used to solve problems with over one million unknowns on a single PC. Using this software, an integral equation solver can be made matrix-free. Hence, the entire matrix representation of the integral operator need not be stored. The resultant storage requirement is O(N). Moreover, the matrix-vector product can be achieved in O(N log N) to O(N) operations.

Integral equations are first converted to a matrix equation using the method of moments (MOM). The matrix equation is fully populated and is difficult and expensive to solve and store when the number of unknowns becomes large. However, FMALib can accelerate the matrix-vector product of the matrix equation. Hence, when used together with an iterative solver such as the conjugate gradient (CG), GMRES methods, an integral equation can be solved orders of magnitude faster than the traditional methods of solving matrix equations resulting from MOM.

This work has supported three other PhD works. See more supplementary materials by clicking here.

Get additional resource on how to use FMALib by clicking here.

Please acknowledge the following works if you find this useful.


  1. L.J. Jiang and W.C. Chew, "A mixed-form fast multipole algorithm," IEEE Trans. Antennas Propag., vol. AP-53, no. 12, pp. 4145-4156, December, 2005.
  2. L.J. Jiang, "Studies on low frequency fast multipole algorithms," Ph.D. Thesis, Dept. ECE, U. Illinois, Urbana-Champaign, August 2004.
  3. Z.G. Qian, and W. C. Chew, "Fast full-wave surface integral equation solver for multiscale structure modeling," IEEE Trans. Antennas and Propagat. , vol. 57, no. 11, pp. 3594-3601, Nov. 2009.
  4. Z.G. Qian, "Augmented surface integral equation method for low-frequency electromagnetic analysis," Ph.D. Thesis. Dept. ECE, U. Illinois, Urbana-Champaign, IL, 2009.