This paper proposes improvements in the row and column samplings of the multilevel QR factorization method known as IES/sup 3/, a fast integral equation solver previously proposed for efficient three-dimensional (3-D) parameter extraction. First, a rigorous Gram-Schmidt row sampling is developed to replace the row sampling algorithm in IES/sup 3/, leading to a more stable algorithm. Second, to further enhance the efficiency of column sampling, a new scheme based on the idea of locating the interpolation points is presented. Error analyses indicate that the proposed schemes have higher accuracies than the original sampling in IES/sup 3/, especially when the number of sampled points is small. The IES/sup 3/ that uses one of these improved algorithms is called improved multilevel matrix QR factorization (IMLMQRF). These IMLMQRFs are applied in the magnetoquasistatic analysis of printed circuits on multilayered lossy medium for extractions of inductances and resistances. The frequency dependency of such parameters is also illustrated.

In this paper, a new multilevel Green's function interpolation method (MLGFIM) is presented to solve integral equations for large-scale electrostatic problems. In MLGFIM, the problem domain is first divided into multilevel cubes. Next, the peer-level Green's function interpolation technique is employed, and then, a new lower-to-upper-level Green's function interpolation technique is devised. They are used with the multilevel discretization to speed up the matrix-vector multiplications in the iterative solution in which a computational complexity of O(N) is achieved. The MLGFIM is used to extract the capacitances encountered in radio frequency integrated circuits (RFICs) and microelectromechanical systems. Moreover, to demonstrate its efficiency both in simulation speed and memory storage requirement, MLGFIM is compared with FastCap for free space problems and applied to extract capacitances from multilayered structures. For problems with 375,000 unknowns, the proposed method only requires 343 MB of computer memory.