Integral equation solution of Maxwell's equations from zero frequency to microwave frequencies

We develop a new method to precondition the matrix equation resulting from applying the method of moments (MoM) to the electric field integral equation (EFIE). This preconditioning method is based on first applying the loop-tree or loop-star decomposition of the currents to arrive at a Helmholtz dec...

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Bibliographic Details
Published in:IEEE transactions on antennas and propagation 2000-10, Vol.48 (10), p.1635-1645
Main Authors: Zhao, Jun-Sheng, Chew, Weng Cho
Format: Article
Language:English
Subjects:
Algorithms
Biomedical optical imaging
Decomposition
Electromagnetics
Geometry
Integral equations
Joints
Mathematical analysis
Matrix decomposition
Maxwell equations
Maxwell's equations
Microwave frequencies
Moment methods
Optical sensors
Preconditioning
Radar antennas
Solvers
Studies
Transformations
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Summary:We develop a new method to precondition the matrix equation resulting from applying the method of moments (MoM) to the electric field integral equation (EFIE). This preconditioning method is based on first applying the loop-tree or loop-star decomposition of the currents to arrive at a Helmholtz decomposition of the unknown currents. However, the MoM matrix thus obtained still cannot be solved efficiently by iterative solvers due to the large number of iterations required. We propose a permutation of the loop-tree or loop-star currents by a connection matrix, to arrive at a current basis that yields a MoM matrix that can be solved efficiently by iterative solvers. Consequently, dramatic reduction in iteration count has been observed. The various steps can be regarded as a rearrangement of the basis functions to arrive at the MoM matrix. Therefore, they are related to the original MoM matrix by matrix transformation, where the transformation requires the inverse of the connection matrix. We have also developed a fast method to invert the connection matrix so that the complexity of the preconditioning procedure is of O(N) and, hence, can be used in fast solvers such as the low-frequency multilevel fast multipole algorithm (LP-MLFMA). This procedure also makes viable the use of fast solvers such as MLFMA to seek the iterative solutions of Maxwell's equations from zero frequency to microwave frequencies.
ISSN:0018-926X
1558-2221
DOI:10.1109/8.899680