A fast matrix equation solver for electrically small structures

Abstract

In this project, I want to improve the Multilevel QR Factorization Method (MLMQRF), a fast integral equation solver for electrically small structures. First, the Gram-Schmidt sampling algorithm was modified to reduce the time consumption for interpolated sampling and QR decomposition. Second, another iterative method, Quasi Minimal Residual (QMR), was adopted to check the iterative scheme performance besides the conventional Conjugate Gradient (CG) and Bi-Conjugate Gradient methods. Third, to further reduce the time for sampling, marginal sampling scheme based on interpolation techniques was investigated. The comparisons of time consumption among different algorithms indicated that the improved schemes have faster speed than the original MLMQRF (50% time consumption). These improved MLMQRFs could be applied in 2D and 3D magnetoquasistatic analysis of RFICs for the calculation of inductances and resistances. The frequency response of inductances and resistances was also illustrated.