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The adaptive integral method (AIM) is implemented in conjunction with the loop-tree (LT) decomposition of the electric current density in the method of moments approximation of the electric field integral equation. The representation of the unknown currents in terms of its solenoidal and irrotational components allows for accurate, broadband electromagnetic (EM) simulation without low-frequency numerical instability problems, while scaling of computational complexity and memory storage with the size of the problem of the are of the same order as in the conventional AIM algorithm. The proposed algorithm is built as an extension to the conventional AIM formulation that utilizes roof-top expansion functions, thus providing direct and easy way for the development of the new stable formulation when the roof-top based AIM is available. A new preconditioning strategy utilizing near interactions in the system which are typically available in the implementation of fast solvers is proposed and tested. The discussed preconditioner can be used with both roof-top and LT formulations of AIM and other fast algorithms. The resulting AIM implementation is validated through its application to the broadband, EM analysis of large microstrip antennas and planar interconnect structures. Index Terms--Fast algorithms, full-wave electromagnetic (EM) CAD, loop-tree (LT) decomposition, low frequency, method of moments (MoM).

The performance of integral-equation-based fast iterative solution schemes such as the adaptive integral method (AIM) and the conjugate gradient (CG) fast Fourier transform (FFT) algorithm can be substantially improved at low frequencies if the electric current and electric charge densities are treated as two separate unknown quantities. The representation of the current density in terms of solenoidal expansion functions (loops) and the charge density in terms of pulse basis functions provides for an exact decomposition of the original electromagnetic (EM) boundary-value problem into its magnetostatic and electrostatic forms at zero frequency. This formulation allows for accurate EM modeling down to very low frequencies free of numerical instabilities, while the spectral properties of the matrix equation are substantially improved compared to the standard method of moments formulation in either loop-tree or loop-star basis. The AIM and the CG FFT algorithms can be appropriately adjusted to accommodate for the use of loop-charge basis functions, thus leading to efficient solvers with O(N log N) solution complexity and O(N) memory requirements for two-and-one-half-dimensional and penetrable three-dimensional (3-D) structures. For general 3-D objects, the CPU time and memory of the algorithms scale as O([N.sup.1.5] log N) and O([N.sup.1.5]), respectively. The new implementation of the AIM is discussed and demonstrated through its application for the broad-band simulation of complex interconnect and electronic packaging structures. Index Terms--Fast algorithms, full-wave computer-aided design (CAD), loop-charge decomposition, low frequency, method of moments (MoM).

A powerful technique for solving electromagnetic (EM) surface integral equations (SIE5) for inhomogenous objects by the method of moments (MoM) involves the well-known Rao-Wilton-Glisson (RWG) basis function to represent the electric current and, for field orthogonality and numerical stability reasons, a variation of the RWG basis known as the ̂n x RWG basis (where ̂n is a unit normal vector at the object surface) to represent the magnetic current. Though this combination provides a numerically efficient and effective solution that has been demonstrated on a variety of structures, one cannot feel entirely comfortable because of the presence of fictitious magnetic current associated with the modified basis. Chen and Wilton proposed a different, smoother basis in 1990 that avoids the fictitious line charges, but because of computational cost issues it has not been used beyond Chen's dissertation. Recently, this basis was rediscovered and has received considerable attention. Our work reexamines the dual basis, exploring issues not addressed by Chen and Wilton and showing accurate solutions for a variety of EM scattering structures. [ABSTRACT FROM AUTHOR]

In this paper, a fast electromagnetic integral equation solution methodology is proposed for the frequency-domain modeling of lossy, interconnect structures. The proposed method utilizes a two-layer model for thick conductors where the unknown current density inside the rectangular wire strips is approximated in terms of equivalent surface currents placed at the top and bottom sides of the strip which, for the purposes of this paper, are assumed to be substantially larger than the side strips. A matrix impedance relationship, which depends on the conductor thickness and its material properties, is established between the two surface current densities to account for the skin effect behavior of the field within the conductor. The selected assignment of the unknown current densities on the planes associated with the top and bottom sides of the metallization, combined with the planarity of multilayered interconnect structures, makes possible the application of the conjugate gradient fast Fourier transform (FFT) algorithm for the computationally efficient prediction of the electromagnetic response of multiport interconnect structures. Applications of the resulting fast integral equation solver to the electromagnetic modeling of interconnect circuits with thick lossy conductors from near dc to multigigahertz frequencies are used to demonstrate the validity of the method and quantify its computational efficiency. [ABSTRACT FROM AUTHOR]

Presents a reply to the comments made on the article "On Deembedding of Port Discontinuities in Full-Wave CAD Models of Multiport Circuits," published in the previous issue of the journal "IEEE Transactions on Microwave Theory and Techniques."