@inproceedings{cf6e80e344a54f43918848013d5a66b8,
title = "Preconditioned adaptive integral method for fast electromagnetic analysis of arrays of through-silicon vias",
abstract = "A preconditioned adaptive integral method is presented for the expedient extraction of the broadband scattering parameters of large arrays of through-silicon vias. The method relies on a proper decomposition of the original kernel functions in the Foldy-Lax based integral equation statement of the pertinent electromagnetic boundary value problem to generate translation-invariant expressions. Thus, Fast-Fourier Transform based convolution can be used for the efficient calculation of the matrix vector products in the Krylov projection-based iterative solution of the sparse matrix equation resulting from the numerical approximation of the governing integral equation. A multi-frontal preconditioner is constructed and implemented for the Krylov projection-based iterative solution of the sparse matrix. The accuracy of the proposed methodology is validated through comparison with HFSS{\texttrademark}-obtained scattering parameters of a simple through-silicon via arrays, while its capacity in handling large arrays is demonstrated through its application to the analysis of a 25×25 TSV array.",
keywords = "Foldy-Lax formulation, Krylov methods, Through-silicon vias, adaptive integral equation method, iterative solution, signal integrity",
author = "Aosheng Rong and Cangellaris, {Andreas C.} and Feng Ling",
year = "2014",
month = jan
day = "1",
doi = "10.1109/MWSYM.2014.6848535",
language = "English (US)",
isbn = "9781479938698",
series = "IEEE MTT-S International Microwave Symposium Digest",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
booktitle = "2014 IEEE MTT-S International Microwave Symposium, IMS 2014",
address = "United States",
note = "2014 IEEE MTT-S International Microwave Symposium, IMS 2014 ; Conference date: 01-06-2014 Through 06-06-2014",
}