Hierarchical vector bases for 3D problems

Roberto D. Graglia; Andrew F. Peterson; Paolo Petrini; Ladislau Matekovits

doi:10.1109/USNC-URSI.2015.7303645

Hierarchical vector bases for 3D problems

Roberto D. Graglia, Andrew F. Peterson, Paolo Petrini, Ladislau Matekovits

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution

Abstract

Hierarchical curl- and divergence-conforming vector bases for two- and three-dimensional cells were derived and discussed in a four paper series published by Graglia, Peterson et al. in the IEEE Trans. Antennas Propagation ([1] vol. 59, pp. 950-959, 2011; [2] vol. 59, pp. 2766-2773, 2011; [3] vol. 60, pp. 3314-3324, 2012; [4] vol. 60, pp. 5215-5227, 2012). Relatively few results for 3D problems are reported in these papers due to an emphasis on (a) the procedures used to derive the hierarchical vector bases and (b) the linear independence of the basis functions. Conversely, results for two-dimensional problems obtained using hierarchical vector bases functions on triangular and quadrilateral cells are reported in two short papers by Peterson and Graglia ([5] 'Scale factors and matrix conditioning associated with triangular-cell hierarchical vector basis functions,' IEEE AWPL, vol. 9, pp. 40-43, 2010. [6] 'Evaluation of hierarchical vector basis functions for quadrilateral cells' IEEE Trans. Mag., vol. 47, no. 5, pp. 1190-1193, 2011).

Original language	English
Title of host publication	2015 USNC-URSI Radio Science Meeting (Joint with AP-S Symposium), USNC-URSI 2015 - Proceedings
Place of Publication	Piscataway, NJ
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	361
Number of pages	1
ISBN (Electronic)	9781479978175
ISBN (Print)	9781479978182
DOIs	https://doi.org/10.1109/USNC-URSI.2015.7303645
Publication status	Published - 21 Oct 2015
Externally published	Yes
Event	USNC-URSI Radio Science Meeting (Joint with AP-S Symposium), USNC-URSI 2015 - Vancouver, Canada Duration: 19 Jul 2015 → 24 Jul 2015

Other

Other	USNC-URSI Radio Science Meeting (Joint with AP-S Symposium), USNC-URSI 2015
Country/Territory	Canada
City	Vancouver
Period	19/07/15 → 24/07/15

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10.1109/USNC-URSI.2015.7303645

Cite this

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title = "Hierarchical vector bases for 3D problems",

abstract = "Hierarchical curl- and divergence-conforming vector bases for two- and three-dimensional cells were derived and discussed in a four paper series published by Graglia, Peterson et al. in the IEEE Trans. Antennas Propagation ([1] vol. 59, pp. 950-959, 2011; [2] vol. 59, pp. 2766-2773, 2011; [3] vol. 60, pp. 3314-3324, 2012; [4] vol. 60, pp. 5215-5227, 2012). Relatively few results for 3D problems are reported in these papers due to an emphasis on (a) the procedures used to derive the hierarchical vector bases and (b) the linear independence of the basis functions. Conversely, results for two-dimensional problems obtained using hierarchical vector bases functions on triangular and quadrilateral cells are reported in two short papers by Peterson and Graglia ([5] 'Scale factors and matrix conditioning associated with triangular-cell hierarchical vector basis functions,' IEEE AWPL, vol. 9, pp. 40-43, 2010. [6] 'Evaluation of hierarchical vector basis functions for quadrilateral cells' IEEE Trans. Mag., vol. 47, no. 5, pp. 1190-1193, 2011).",

author = "Graglia, {Roberto D.} and Peterson, {Andrew F.} and Paolo Petrini and Ladislau Matekovits",

year = "2015",

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Graglia, RD, Peterson, AF, Petrini, P & Matekovits, L 2015, Hierarchical vector bases for 3D problems. in 2015 USNC-URSI Radio Science Meeting (Joint with AP-S Symposium), USNC-URSI 2015 - Proceedings., 7303645, Institute of Electrical and Electronics Engineers (IEEE), Piscataway, NJ, pp. 361, USNC-URSI Radio Science Meeting (Joint with AP-S Symposium), USNC-URSI 2015, Vancouver, Canada, 19/07/15. https://doi.org/10.1109/USNC-URSI.2015.7303645

Hierarchical vector bases for 3D problems. / Graglia, Roberto D.; Peterson, Andrew F.; Petrini, Paolo et al.
2015 USNC-URSI Radio Science Meeting (Joint with AP-S Symposium), USNC-URSI 2015 - Proceedings. Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE), 2015. p. 361 7303645.

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution

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T1 - Hierarchical vector bases for 3D problems

AU - Graglia, Roberto D.

AU - Peterson, Andrew F.

AU - Petrini, Paolo

AU - Matekovits, Ladislau

PY - 2015/10/21

Y1 - 2015/10/21

N2 - Hierarchical curl- and divergence-conforming vector bases for two- and three-dimensional cells were derived and discussed in a four paper series published by Graglia, Peterson et al. in the IEEE Trans. Antennas Propagation ([1] vol. 59, pp. 950-959, 2011; [2] vol. 59, pp. 2766-2773, 2011; [3] vol. 60, pp. 3314-3324, 2012; [4] vol. 60, pp. 5215-5227, 2012). Relatively few results for 3D problems are reported in these papers due to an emphasis on (a) the procedures used to derive the hierarchical vector bases and (b) the linear independence of the basis functions. Conversely, results for two-dimensional problems obtained using hierarchical vector bases functions on triangular and quadrilateral cells are reported in two short papers by Peterson and Graglia ([5] 'Scale factors and matrix conditioning associated with triangular-cell hierarchical vector basis functions,' IEEE AWPL, vol. 9, pp. 40-43, 2010. [6] 'Evaluation of hierarchical vector basis functions for quadrilateral cells' IEEE Trans. Mag., vol. 47, no. 5, pp. 1190-1193, 2011).

AB - Hierarchical curl- and divergence-conforming vector bases for two- and three-dimensional cells were derived and discussed in a four paper series published by Graglia, Peterson et al. in the IEEE Trans. Antennas Propagation ([1] vol. 59, pp. 950-959, 2011; [2] vol. 59, pp. 2766-2773, 2011; [3] vol. 60, pp. 3314-3324, 2012; [4] vol. 60, pp. 5215-5227, 2012). Relatively few results for 3D problems are reported in these papers due to an emphasis on (a) the procedures used to derive the hierarchical vector bases and (b) the linear independence of the basis functions. Conversely, results for two-dimensional problems obtained using hierarchical vector bases functions on triangular and quadrilateral cells are reported in two short papers by Peterson and Graglia ([5] 'Scale factors and matrix conditioning associated with triangular-cell hierarchical vector basis functions,' IEEE AWPL, vol. 9, pp. 40-43, 2010. [6] 'Evaluation of hierarchical vector basis functions for quadrilateral cells' IEEE Trans. Mag., vol. 47, no. 5, pp. 1190-1193, 2011).

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BT - 2015 USNC-URSI Radio Science Meeting (Joint with AP-S Symposium), USNC-URSI 2015 - Proceedings

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T2 - USNC-URSI Radio Science Meeting (Joint with AP-S Symposium), USNC-URSI 2015

Y2 - 19 July 2015 through 24 July 2015

ER -

Hierarchical vector bases for 3D problems

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