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ACAsolver Software

Adaptive Cross Approximation (ACA) integration into existing MoM codes


Juan M. Rius with J. M. Tamayo, A. Heldring, J. Parrón and E. Ubeda


The authors are (or have been) with AntennaLab, Dept. of Signal Theory and Communications, Universitat Politecnica de Catalunya, Barcelona, Spain.


e-mail:  ( )



ACAsolver is a fast iterative solver for compressible linear systems, with multilevel Adaptive Cross Approximation (ACA) matrix compression. ACA is based on the fact that interaction between far-field spatial subdomains has a reduced number of degrees of freedom. Although the solver has been developed for Electromagnetic Integral Equation problems discretized by Method of Moments (MoM), it can be applied to any physics or engineering linear system of equations with a compressible matrix that contains rank-deficient pseudo-submatrices.


We believe that software integration between University research groups is the key for successful analysis of very complex antenna configurations, that cannot be handled yet by commercial Computational Electromagnetics (CEM) packages. The integration effort started in Antennas Center of Excellence (ACE) network can be the seed of a future Linux-like open library of CEM engines and solvers.


Adaptive Cross Approximation (ACA):

Among many matrix compression algorithms that have been used by the CEM community to accelerate the solution of MoM linear systems, we have chosen ACA because it is -to our knowledge- the simplest to integrate with existing MoM codes.


Selected key references:


  • M. Bebendorf, “Approximation of boundary element matrices”, Numer. Math., vol. 86, no. 4, pp. 565–589, 2000.
  • K. Zhao, M. Vouvakis, and J.-F. Lee, “The adaptive cross approximation algorithm for accelerated method of moment computations of emc problems”, IEEE Trans. on Electromagnetic Compatibility, vol. 47, no. 4, pp. 763–773, Nov. 2005.



             ACAsolver 1.0.3 with MoM-2D EFIE-TM example (MATLAB)


             ACAsolver 1.1.2 with MoM-3D example (MATLAB)


             ACAsolver 1.0 user guide


Planned next release:

Pyhton-scipy version of ACAsolver 1.0.


License terms:


ACAsolver block diagram: