00000cab a22000003a 4500 UP-99796217609467703 Buklod 20231007234322.0 m |o d | ta 100921s xx d | ||r ||||| || DENGII eng Jun-Sheng Zhao Integral equation solution of Maxwell's equations from zero frequency to microwave frequencies. pp. 1635-1645 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 EFIE. Helmholtz decomposition. Maxwell's equations. MoM matrix. Basis functions. Complexity. Conducting bodies. Connection matrix. Electric field integral equation. Fast solvers. Integral equation solution. Inverse connection matrix. Iterative solvers. Loop-star current. Loop-star decomposition. Loop-tree current. Loop-tree decomposition. Low-frequency multilevel fast multipole algorithm. Matrix equation preconditioning. Matrix transformation. Method of moments. Microwave frequencies. Permutation. IEEE Transactions on antennas and propagation 48, 10 (2000). FO UPD DENG-II Article