Smooth local cosine based Galerkin method for scattering problems

George W. Pan; Youri V. Tretiakov; Barry Gilbert

doi:10.1109/TAP.2003.809086

Smooth local cosine based Galerkin method for scattering problems

George W. Pan, Youri V. Tretiakov, Barry Gilbert

Physiology & Biomedical Engineering

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

The smooth local trigonometric (SLT) functions are employed as the basis and testing functions in the Galerkin based method of moments (MoM), and sparse impedance matrices are obtained. The basic idea of SLT is to use smooth cutoff functions to split the function and to fold overlapping parts back into the intervals so that the orthogonality of the system is preserved. Moreover, by choosing the correct trigonometric basis, rapid convergence in the case of smooth functions is ensured. The SLT system is particularly suitable to handle electrically large scatterers, where the integral kernel behaves in a highly oscillatory manner. Numerical examples demonstrate the scattering of electromagnetic waves from two-dimensional objects with smooth contours as well as with sharp edges. A comparison of the new approach versus the traditional MoM and wavelet methods is provided.

Original language	English (US)
Pages (from-to)	1177-1184
Number of pages	8
Journal	IEEE Transactions on Antennas and Propagation
Volume	51
Issue number	6
DOIs	https://doi.org/10.1109/TAP.2003.809086
State	Published - Jun 2003

Keywords

Method of moments (MoM)
Scattering coefficients
Smooth local cosine (SLC)
Wavelets

ASJC Scopus subject areas

Electrical and Electronic Engineering

Access to Document

10.1109/TAP.2003.809086

Cite this

@article{401fbae9f7294458b0a5ab7e6ffa6073,

title = "Smooth local cosine based Galerkin method for scattering problems",

abstract = "The smooth local trigonometric (SLT) functions are employed as the basis and testing functions in the Galerkin based method of moments (MoM), and sparse impedance matrices are obtained. The basic idea of SLT is to use smooth cutoff functions to split the function and to fold overlapping parts back into the intervals so that the orthogonality of the system is preserved. Moreover, by choosing the correct trigonometric basis, rapid convergence in the case of smooth functions is ensured. The SLT system is particularly suitable to handle electrically large scatterers, where the integral kernel behaves in a highly oscillatory manner. Numerical examples demonstrate the scattering of electromagnetic waves from two-dimensional objects with smooth contours as well as with sharp edges. A comparison of the new approach versus the traditional MoM and wavelet methods is provided.",

keywords = "Method of moments (MoM), Scattering coefficients, Smooth local cosine (SLC), Wavelets",

author = "Pan, {George W.} and Tretiakov, {Youri V.} and Barry Gilbert",

note = "Funding Information: Manuscript received July 22, 2000; revised November 26, 2001. This work was supported in part by the Microsystems Technology Office and the Defense Science Office (DARPA/MTO) of the Defense Advanced Research Projects Agency DARPA/DSO) through Contract N66001-99-C-8605 from SPAWAR Systems Center San Diego. G. W. Pan is with the Electronic Packaging Laboratory, Telecommunications Research Center, Arizona State University, Tempe, AZ 85287–7206 USA (e-mail: george.pan@asu.edu). Y. V. Tretiakov is with IBM Microelectronics, Essex Junction, VT 05452 USA (e-mail: yourit@us.ibm.com). B. Gilbert is with the Mayo Foundation, Rochester, MN 55905 USA. Digital Object Identifier 10.1109/TAP.2003.809086",

year = "2003",

month = jun,

doi = "10.1109/TAP.2003.809086",

language = "English (US)",

volume = "51",

pages = "1177--1184",

journal = "IEEE Transactions on Antennas and Propagation",

issn = "0018-926X",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "6",

}

TY - JOUR

T1 - Smooth local cosine based Galerkin method for scattering problems

AU - Pan, George W.

AU - Tretiakov, Youri V.

AU - Gilbert, Barry

N1 - Funding Information: Manuscript received July 22, 2000; revised November 26, 2001. This work was supported in part by the Microsystems Technology Office and the Defense Science Office (DARPA/MTO) of the Defense Advanced Research Projects Agency DARPA/DSO) through Contract N66001-99-C-8605 from SPAWAR Systems Center San Diego. G. W. Pan is with the Electronic Packaging Laboratory, Telecommunications Research Center, Arizona State University, Tempe, AZ 85287–7206 USA (e-mail: george.pan@asu.edu). Y. V. Tretiakov is with IBM Microelectronics, Essex Junction, VT 05452 USA (e-mail: yourit@us.ibm.com). B. Gilbert is with the Mayo Foundation, Rochester, MN 55905 USA. Digital Object Identifier 10.1109/TAP.2003.809086

PY - 2003/6

Y1 - 2003/6

N2 - The smooth local trigonometric (SLT) functions are employed as the basis and testing functions in the Galerkin based method of moments (MoM), and sparse impedance matrices are obtained. The basic idea of SLT is to use smooth cutoff functions to split the function and to fold overlapping parts back into the intervals so that the orthogonality of the system is preserved. Moreover, by choosing the correct trigonometric basis, rapid convergence in the case of smooth functions is ensured. The SLT system is particularly suitable to handle electrically large scatterers, where the integral kernel behaves in a highly oscillatory manner. Numerical examples demonstrate the scattering of electromagnetic waves from two-dimensional objects with smooth contours as well as with sharp edges. A comparison of the new approach versus the traditional MoM and wavelet methods is provided.

AB - The smooth local trigonometric (SLT) functions are employed as the basis and testing functions in the Galerkin based method of moments (MoM), and sparse impedance matrices are obtained. The basic idea of SLT is to use smooth cutoff functions to split the function and to fold overlapping parts back into the intervals so that the orthogonality of the system is preserved. Moreover, by choosing the correct trigonometric basis, rapid convergence in the case of smooth functions is ensured. The SLT system is particularly suitable to handle electrically large scatterers, where the integral kernel behaves in a highly oscillatory manner. Numerical examples demonstrate the scattering of electromagnetic waves from two-dimensional objects with smooth contours as well as with sharp edges. A comparison of the new approach versus the traditional MoM and wavelet methods is provided.

KW - Method of moments (MoM)

KW - Scattering coefficients

KW - Smooth local cosine (SLC)

KW - Wavelets

UR - http://www.scopus.com/inward/record.url?scp=0038721569&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038721569&partnerID=8YFLogxK

U2 - 10.1109/TAP.2003.809086

DO - 10.1109/TAP.2003.809086

M3 - Article

AN - SCOPUS:0038721569

SN - 0018-926X

VL - 51

SP - 1177

EP - 1184

JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

IS - 6

ER -

Smooth local cosine based Galerkin method for scattering problems

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this