Low Rank Matrix Algebra for the Method of Moments
Keywords:
ACA, Direct Factor Method of Moments, electromagnetic scattering, Rk mathAbstract
This tutorial presents the use of low rank Rk matrix block formulations for advancing the problem size capability N of the Method of Moments full wave approach to solving Maxwell’s integral equations. When MOM unknowns are spatially grouped, the group-group interaction matrix blocks become low rank for electrically large problems. A very significant advantage of this Rk property along with use of the Adaptive Cross Approximation leads to dramatic reduction in memory storage and in operations count. While early Rk approaches focused on iterative approaches, this work shows how Rk methods can be applied to direct solve LU factorization approaches and, for scattering problems, Rk methods can be used to compute the full polarization scattering matrix.
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References
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