Dramatic improvements in the matrix solution time for method of moment problems involving stripline interconnects

Xing Wang, Zhaohui Zhu, Yi Cao, Steven L Dvorak, John L. Prince

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Method of moments (MoM) reaction matrices are typically thought of as being full matrices in most applications. However, in this paper, we demonstrate for the first time that sparse reaction matrices are produced when modeling stripline interconnects provided that a parallel-plate Green's function is employed in the analysis. This is demonstrated by investigating the sparse nature of the MoM reaction matrices that are produced when using the full-wave layered interconnect solver (UA-FWLIS) to model stripline interconnects. In order to explain the sparse nature of the reaction matrices, the electric fields that are excited by horizontal and vertical electric dipole sources are briefly overviewed, and the cutoff mode behavior of these electric fields is studied. Then the variations of the reaction elements with distance are studied, and this information is used to provide a cutoff criterion for the reaction element calculations. Once the reasons for the matrix sparsity have been explained, then we test various matrix solution algorithms in order to determine their efficiencies. We found that by applying sparse matrix storage techniques and a sparse matrix solver, it is possible to dramatically improve the matrix solution time when compared with a commercial MoM-based simulator.

Original languageEnglish (US)
Pages (from-to)570-579
Number of pages10
JournalIEEE Transactions on Advanced Packaging
Volume30
Issue number3
DOIs
StatePublished - Aug 2007

Fingerprint

Method of moments
Electric fields
Green's function
Simulators

Keywords

  • Conjugate gradient
  • Integral equation
  • Interconnects
  • Method of moments (MOM)
  • Sparse matrix
  • Stripline

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Industrial and Manufacturing Engineering
  • Materials Science(all)

Cite this

Dramatic improvements in the matrix solution time for method of moment problems involving stripline interconnects. / Wang, Xing; Zhu, Zhaohui; Cao, Yi; Dvorak, Steven L; Prince, John L.

In: IEEE Transactions on Advanced Packaging, Vol. 30, No. 3, 08.2007, p. 570-579.

Research output: Contribution to journalArticle

@article{a548452d71674458ac5450b44c1494cb,
title = "Dramatic improvements in the matrix solution time for method of moment problems involving stripline interconnects",
abstract = "Method of moments (MoM) reaction matrices are typically thought of as being full matrices in most applications. However, in this paper, we demonstrate for the first time that sparse reaction matrices are produced when modeling stripline interconnects provided that a parallel-plate Green's function is employed in the analysis. This is demonstrated by investigating the sparse nature of the MoM reaction matrices that are produced when using the full-wave layered interconnect solver (UA-FWLIS) to model stripline interconnects. In order to explain the sparse nature of the reaction matrices, the electric fields that are excited by horizontal and vertical electric dipole sources are briefly overviewed, and the cutoff mode behavior of these electric fields is studied. Then the variations of the reaction elements with distance are studied, and this information is used to provide a cutoff criterion for the reaction element calculations. Once the reasons for the matrix sparsity have been explained, then we test various matrix solution algorithms in order to determine their efficiencies. We found that by applying sparse matrix storage techniques and a sparse matrix solver, it is possible to dramatically improve the matrix solution time when compared with a commercial MoM-based simulator.",
keywords = "Conjugate gradient, Integral equation, Interconnects, Method of moments (MOM), Sparse matrix, Stripline",
author = "Xing Wang and Zhaohui Zhu and Yi Cao and Dvorak, {Steven L} and Prince, {John L.}",
year = "2007",
month = "8",
doi = "10.1109/TADVP.2007.898638",
language = "English (US)",
volume = "30",
pages = "570--579",
journal = "IEEE Transactions on Advanced Packaging",
issn = "1521-3323",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "3",

}

TY - JOUR

T1 - Dramatic improvements in the matrix solution time for method of moment problems involving stripline interconnects

AU - Wang, Xing

AU - Zhu, Zhaohui

AU - Cao, Yi

AU - Dvorak, Steven L

AU - Prince, John L.

PY - 2007/8

Y1 - 2007/8

N2 - Method of moments (MoM) reaction matrices are typically thought of as being full matrices in most applications. However, in this paper, we demonstrate for the first time that sparse reaction matrices are produced when modeling stripline interconnects provided that a parallel-plate Green's function is employed in the analysis. This is demonstrated by investigating the sparse nature of the MoM reaction matrices that are produced when using the full-wave layered interconnect solver (UA-FWLIS) to model stripline interconnects. In order to explain the sparse nature of the reaction matrices, the electric fields that are excited by horizontal and vertical electric dipole sources are briefly overviewed, and the cutoff mode behavior of these electric fields is studied. Then the variations of the reaction elements with distance are studied, and this information is used to provide a cutoff criterion for the reaction element calculations. Once the reasons for the matrix sparsity have been explained, then we test various matrix solution algorithms in order to determine their efficiencies. We found that by applying sparse matrix storage techniques and a sparse matrix solver, it is possible to dramatically improve the matrix solution time when compared with a commercial MoM-based simulator.

AB - Method of moments (MoM) reaction matrices are typically thought of as being full matrices in most applications. However, in this paper, we demonstrate for the first time that sparse reaction matrices are produced when modeling stripline interconnects provided that a parallel-plate Green's function is employed in the analysis. This is demonstrated by investigating the sparse nature of the MoM reaction matrices that are produced when using the full-wave layered interconnect solver (UA-FWLIS) to model stripline interconnects. In order to explain the sparse nature of the reaction matrices, the electric fields that are excited by horizontal and vertical electric dipole sources are briefly overviewed, and the cutoff mode behavior of these electric fields is studied. Then the variations of the reaction elements with distance are studied, and this information is used to provide a cutoff criterion for the reaction element calculations. Once the reasons for the matrix sparsity have been explained, then we test various matrix solution algorithms in order to determine their efficiencies. We found that by applying sparse matrix storage techniques and a sparse matrix solver, it is possible to dramatically improve the matrix solution time when compared with a commercial MoM-based simulator.

KW - Conjugate gradient

KW - Integral equation

KW - Interconnects

KW - Method of moments (MOM)

KW - Sparse matrix

KW - Stripline

UR - http://www.scopus.com/inward/record.url?scp=34548188757&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34548188757&partnerID=8YFLogxK

U2 - 10.1109/TADVP.2007.898638

DO - 10.1109/TADVP.2007.898638

M3 - Article

AN - SCOPUS:34548188757

VL - 30

SP - 570

EP - 579

JO - IEEE Transactions on Advanced Packaging

JF - IEEE Transactions on Advanced Packaging

SN - 1521-3323

IS - 3

ER -