A higher order space-time Galerkin scheme for time domain integral equations

Andrew J. Pray; Yves Beghein; Naveen V. Nair; Kristof Cools; Hakan Bagci; Balasubramaniam Shanker

doi:10.1109/TAP.2014.2361156

A higher order space-time Galerkin scheme for time domain integral equations

Andrew J. Pray, Yves Beghein, Naveen V. Nair, Kristof Cools, Hakan Bagci, Balasubramaniam Shanker

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

18 Scopus citations

Abstract

Stability of time domain integral equation (TDIE) solvers has remained an elusive goal formany years. Advancement of this research has largely progressed on four fronts: 1) Exact integration, 2) Lubich quadrature, 3) smooth temporal basis functions, and 4) space-time separation of convolutions with the retarded potential. The latter method's efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was previously reported for first-order surface descriptions (flat elements) and zeroth-order functions as the temporal basis. In this work, we develop the methodology necessary to extend the scheme to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. These basis functions are then used in a space-time Galerkin framework. A number of results are presented that demonstrate convergence in time. The viability of the space-time separation method in producing stable results is demonstrated experimentally for these examples.

Original language	English (US)
Pages (from-to)	6183-6191
Number of pages	9
Journal	IEEE Transactions on Antennas and Propagation
Volume	62
Issue number	12
DOIs	https://doi.org/10.1109/TAP.2014.2361156
State	Published - Dec 2014

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work was supported in part by the NSFunder Grant CCF1018516 and in part by the DoD SMART Program under Grant N00244-09-1-0081.

ASJC Scopus subject areas

Electrical and Electronic Engineering
Condensed Matter Physics

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10.1109/TAP.2014.2361156

Cite this

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title = "A higher order space-time Galerkin scheme for time domain integral equations",

abstract = "Stability of time domain integral equation (TDIE) solvers has remained an elusive goal formany years. Advancement of this research has largely progressed on four fronts: 1) Exact integration, 2) Lubich quadrature, 3) smooth temporal basis functions, and 4) space-time separation of convolutions with the retarded potential. The latter method's efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was previously reported for first-order surface descriptions (flat elements) and zeroth-order functions as the temporal basis. In this work, we develop the methodology necessary to extend the scheme to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. These basis functions are then used in a space-time Galerkin framework. A number of results are presented that demonstrate convergence in time. The viability of the space-time separation method in producing stable results is demonstrated experimentally for these examples.",

author = "Pray, {Andrew J.} and Yves Beghein and Nair, {Naveen V.} and Kristof Cools and Hakan Bagci and Balasubramaniam Shanker",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: This work was supported in part by the NSFunder Grant CCF1018516 and in part by the DoD SMART Program under Grant N00244-09-1-0081.",

year = "2014",

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T1 - A higher order space-time Galerkin scheme for time domain integral equations

AU - Pray, Andrew J.

AU - Beghein, Yves

AU - Nair, Naveen V.

AU - Cools, Kristof

AU - Bagci, Hakan

AU - Shanker, Balasubramaniam

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: This work was supported in part by the NSFunder Grant CCF1018516 and in part by the DoD SMART Program under Grant N00244-09-1-0081.

PY - 2014/12

Y1 - 2014/12

N2 - Stability of time domain integral equation (TDIE) solvers has remained an elusive goal formany years. Advancement of this research has largely progressed on four fronts: 1) Exact integration, 2) Lubich quadrature, 3) smooth temporal basis functions, and 4) space-time separation of convolutions with the retarded potential. The latter method's efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was previously reported for first-order surface descriptions (flat elements) and zeroth-order functions as the temporal basis. In this work, we develop the methodology necessary to extend the scheme to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. These basis functions are then used in a space-time Galerkin framework. A number of results are presented that demonstrate convergence in time. The viability of the space-time separation method in producing stable results is demonstrated experimentally for these examples.

AB - Stability of time domain integral equation (TDIE) solvers has remained an elusive goal formany years. Advancement of this research has largely progressed on four fronts: 1) Exact integration, 2) Lubich quadrature, 3) smooth temporal basis functions, and 4) space-time separation of convolutions with the retarded potential. The latter method's efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was previously reported for first-order surface descriptions (flat elements) and zeroth-order functions as the temporal basis. In this work, we develop the methodology necessary to extend the scheme to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. These basis functions are then used in a space-time Galerkin framework. A number of results are presented that demonstrate convergence in time. The viability of the space-time separation method in producing stable results is demonstrated experimentally for these examples.

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JO - IEEE Transactions on Antennas and Propagation

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ER -

A higher order space-time Galerkin scheme for time domain integral equations

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