Divergence-Conforming Constrained Basis Functions for Hexahedral Volume Elements

Robert A. Pfeiffer; John C. Young; Robert J. Adams

doi:10.1109/TAP.2017.2775288

Divergence-Conforming Constrained Basis Functions for Hexahedral Volume Elements

Robert A. Pfeiffer, John C. Young, Robert J. Adams

Electrical and Computer Engineering

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

3 Scopus citations

Abstract

This communication presents an algebraic method for constructing arbitrary-order, divergence-conforming basis functions on hexahedral volume elements. The appropriate constraints within and on the boundaries of elements are provided. In particular, the handling of faces where quantities are discontinuous is discussed. The resulting bases are numerically characterized in terms of error convergence and system conditioning for a moment method discretization of the electric field volume integral equation for dielectric scatterers. Results show the accuracy of the proposed method as well as the low system matrix condition number that can be maintained as the basis order and mesh discretization are increased.

Original language	English
Article number	8115191
Pages (from-to)	501-504
Number of pages	4
Journal	IEEE Transactions on Antennas and Propagation
Volume	66
Issue number	1
DOIs	https://doi.org/10.1109/TAP.2017.2775288
State	Published - Jan 2018

Bibliographical note

Funding Information:
Manuscript received January 12, 2017; revised July 28, 2017; accepted October 18, 2017. Date of publication November 20, 2017; date of current version January 2, 2018. This work was supported in part by the Office of Naval Research under Grant N00014-15-1-2270. (Corresponding author: John C. Young.) The authors are with the Department of Electrical and Computer Engineering, University of Kentucky, Lexington, KY 40506 USA (e-mail: robert.pfeiffer@uky.edu; john.c.young@uky.edu; rjadams@uky.edu).

Publisher Copyright:
© 1963-2012 IEEE.

Keywords

Basis functions
constrained bases
method of moments (MoM)
volume integral equations

ASJC Scopus subject areas

Electrical and Electronic Engineering

Access to Document

10.1109/TAP.2017.2775288

Cite this

@article{29cdc341862e4b2c9faeaeb296a2f3d3,

title = "Divergence-Conforming Constrained Basis Functions for Hexahedral Volume Elements",

abstract = "This communication presents an algebraic method for constructing arbitrary-order, divergence-conforming basis functions on hexahedral volume elements. The appropriate constraints within and on the boundaries of elements are provided. In particular, the handling of faces where quantities are discontinuous is discussed. The resulting bases are numerically characterized in terms of error convergence and system conditioning for a moment method discretization of the electric field volume integral equation for dielectric scatterers. Results show the accuracy of the proposed method as well as the low system matrix condition number that can be maintained as the basis order and mesh discretization are increased.",

keywords = "Basis functions, constrained bases, method of moments (MoM), volume integral equations",

author = "Pfeiffer, {Robert A.} and Young, {John C.} and Adams, {Robert J.}",

note = "Funding Information: Manuscript received January 12, 2017; revised July 28, 2017; accepted October 18, 2017. Date of publication November 20, 2017; date of current version January 2, 2018. This work was supported in part by the Office of Naval Research under Grant N00014-15-1-2270. (Corresponding author: John C. Young.) The authors are with the Department of Electrical and Computer Engineering, University of Kentucky, Lexington, KY 40506 USA (e-mail: robert.pfeiffer@uky.edu; john.c.young@uky.edu; rjadams@uky.edu). Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

year = "2018",

month = jan,

doi = "10.1109/TAP.2017.2775288",

language = "English",

volume = "66",

pages = "501--504",

number = "1",

}

TY - JOUR

T1 - Divergence-Conforming Constrained Basis Functions for Hexahedral Volume Elements

AU - Pfeiffer, Robert A.

AU - Young, John C.

AU - Adams, Robert J.

N1 - Funding Information: Manuscript received January 12, 2017; revised July 28, 2017; accepted October 18, 2017. Date of publication November 20, 2017; date of current version January 2, 2018. This work was supported in part by the Office of Naval Research under Grant N00014-15-1-2270. (Corresponding author: John C. Young.) The authors are with the Department of Electrical and Computer Engineering, University of Kentucky, Lexington, KY 40506 USA (e-mail: robert.pfeiffer@uky.edu; john.c.young@uky.edu; rjadams@uky.edu). Publisher Copyright: © 1963-2012 IEEE.

PY - 2018/1

Y1 - 2018/1

N2 - This communication presents an algebraic method for constructing arbitrary-order, divergence-conforming basis functions on hexahedral volume elements. The appropriate constraints within and on the boundaries of elements are provided. In particular, the handling of faces where quantities are discontinuous is discussed. The resulting bases are numerically characterized in terms of error convergence and system conditioning for a moment method discretization of the electric field volume integral equation for dielectric scatterers. Results show the accuracy of the proposed method as well as the low system matrix condition number that can be maintained as the basis order and mesh discretization are increased.

AB - This communication presents an algebraic method for constructing arbitrary-order, divergence-conforming basis functions on hexahedral volume elements. The appropriate constraints within and on the boundaries of elements are provided. In particular, the handling of faces where quantities are discontinuous is discussed. The resulting bases are numerically characterized in terms of error convergence and system conditioning for a moment method discretization of the electric field volume integral equation for dielectric scatterers. Results show the accuracy of the proposed method as well as the low system matrix condition number that can be maintained as the basis order and mesh discretization are increased.

KW - Basis functions

KW - constrained bases

KW - method of moments (MoM)

KW - volume integral equations

UR - http://www.scopus.com/inward/record.url?scp=85035758527&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85035758527&partnerID=8YFLogxK

U2 - 10.1109/TAP.2017.2775288

DO - 10.1109/TAP.2017.2775288

M3 - Article

AN - SCOPUS:85035758527

VL - 66

SP - 501

EP - 504

IS - 1

M1 - 8115191

ER -

Divergence-Conforming Constrained Basis Functions for Hexahedral Volume Elements

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this