A fast method of moments solver for efficient parameter extraction of MCMs

Abstract

The Method of Moments MoM is often e ectively used i n the extraction of passive components in modeling integrated circuits and MCM packaging. MoM extraction, however, involves solving a dense system of linear equations, and using direct factorization methods can be p r ohibitive for large problems. In this paper, we present a Fast Method of Moments Solver FMMS for the rapid solution of such linear systems. Our algorithm exploits the fact that the integral equation kernels are l o c ally smooth" and can be d r amatically compressed via the singular value decomposition SVD. This greatly speeds up the matrix-vector products in a Krylov-subspace iterative algorithm e.g., GMRES. We demonstrate the e ciency and exibility of our scheme for the modeling of embedded inductors in MCM-D. Results are presented to show that the method i s a c curate and can be two orders of magnitude faster than Gaussian elimination and one order of magnitude faster than standard iterative schemes.

A fast boundary cloud method for exterior 2D electrostatic analysis

“…Compared to the other fast algorithms, SVD-based acceleration technique is much easier to implement as it operates directly on the dense matrix. Even though [22,23] mention that the complexity of the algorithm is O(N log N ) for three-dimensional (3D) problems, our results indicate that the complexity of the approach can be O(N (log N )…”

“…The idea behind the acceleration technique [22,23] is to exploit the fact that the assembled matrix M has large sections which are rank deÿcient. The reason behind this is that, typical Green's functions vary smoothly.…”

“…The complexity of the precorrected FFT algorithm is O(N log N ). Recently, a third method, which uses the concept of singular value decomposition (SVD), is introduced in References [22,23] to compute the dense matrixvector products. This approach utilizes the fact that large parts of integral operator matrix are numerically low rank.…”

A kernel-independent adaptive fast multipole algorithm in two and three dimensions

“…A hybrid method for kernel independent matrix-vector multiplication algorithm was proposed in [16] and [17]. Based on the fact that large blocks of the particle interaction matrix are low rank, this method uses singular value decomposition to sample and sparsify these blocks.…”

A fast boundary cloud method for 3D exterior electrostatic analysis

“…Boundary integral formulations [5] are powerful computational techniques for rapid analysis of exterior problems, especially when combined with fast algorithms based on multipole expansions [6], Fast Fourier transform (FFT) [7] or singular value decomposition (SVD) [8][9][10]. Boundary integral formulations are best suited for exterior electrostatic analysis as they require meshing of the conductor surface only.…”