Loop-tree implementation of the adaptive integral method (AIM) for numerically stable EM modeling from low to multi-GHz frequencies

The Adaptive Integral Method (AIM) is implemented in conjunction with the loop-tree decomposition of the method of moments approximation of the electric field integral equation. The representation of the current in terms of its solenoidal and irrotational components allows for accurate, broadband electromagnetic simulation without any low-frequency numerical instability problems, while the O(NlogN) complexity and O(N) storage of the conventional AIM algorithm are preserved to provide for high computation efficiency. The proposed implementation is numerically validated through its application to the electromagnetic analysis of a microstrip corporate-fed patch antenna array.