Jordan Block Eigenvalue Shift in the Marching-on-in-Time Electric Field Integral Equation

Petrus W.N. Van Diepen; Roeland J. Dilz; Martijn C. Van Beurden

doi:10.23919/EuCAP57121.2023.10133600

Jordan Block Eigenvalue Shift in the Marching-on-in-Time Electric Field Integral Equation

Petrus W.N. Van Diepen, Roeland J. Dilz, Martijn C. Van Beurden

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

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The Marching-on-in-Time Electric Field Integral Equation (MOT-EFIE) and its time differentiated variant (MOT-TDEFIE) both suffer from the linear-in-time instability caused by dimension-two Jordan blocks in the companion-matrix representation. We prove that these Jordan blocks are centered around a specific eigenvalue that depends on the recurrence relation between the interaction matrices. By adapting the recurrence relation, we can move the pertaining eigenvalues of the Jordan blocks to the interior of the unit circle and therefore remove the linear-in-time instability from the scheme. We provide numerical evidence to further illustrate these findings.

Originele taal-2	Engels
Titel	17th European Conference on Antennas and Propagation, EuCAP 2023
Uitgeverij	Institute of Electrical and Electronics Engineers
Pagina's	1-5
Aantal pagina's	5
DOI's	https://doi.org/10.23919/EuCAP57121.2023.10133600
Status	Gepubliceerd - 31 mei 2023
Evenement	17th European Conference on Antennas and Propagation, EuCAP 2023 - Florence, Italië Duur: 26 mrt. 2023 → 31 mrt. 2023

Congres

Congres	17th European Conference on Antennas and Propagation, EuCAP 2023
Land/Regio	Italië
Stad	Florence
Periode	26/03/23 → 31/03/23

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@inproceedings{d7f4390d56594f9dbba94444a1a2fa3b,

title = "Jordan Block Eigenvalue Shift in the Marching-on-in-Time Electric Field Integral Equation",

abstract = "The Marching-on-in-Time Electric Field Integral Equation (MOT-EFIE) and its time differentiated variant (MOT-TDEFIE) both suffer from the linear-in-time instability caused by dimension-two Jordan blocks in the companion-matrix representation. We prove that these Jordan blocks are centered around a specific eigenvalue that depends on the recurrence relation between the interaction matrices. By adapting the recurrence relation, we can move the pertaining eigenvalues of the Jordan blocks to the interior of the unit circle and therefore remove the linear-in-time instability from the scheme. We provide numerical evidence to further illustrate these findings.",

keywords = "companion matrix, electric field integral equation, marching-on-in-time, stability, time domain",

author = "{Van Diepen}, {Petrus W.N.} and Dilz, {Roeland J.} and {Van Beurden}, {Martijn C.}",

year = "2023",

month = may,

day = "31",

doi = "10.23919/EuCAP57121.2023.10133600",

language = "English",

pages = "1--5",

booktitle = "17th European Conference on Antennas and Propagation, EuCAP 2023",

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

note = "17th European Conference on Antennas and Propagation, EuCAP 2023 ; Conference date: 26-03-2023 Through 31-03-2023",

}

Van Diepen, PWN , Dilz, RJ & Van Beurden, MC 2023, Jordan Block Eigenvalue Shift in the Marching-on-in-Time Electric Field Integral Equation. in 17th European Conference on Antennas and Propagation, EuCAP 2023., 10133600, Institute of Electrical and Electronics Engineers, blz. 1-5, 17th European Conference on Antennas and Propagation, EuCAP 2023, Florence, Italië, 26/03/23. https://doi.org/10.23919/EuCAP57121.2023.10133600

Jordan Block Eigenvalue Shift in the Marching-on-in-Time Electric Field Integral Equation. / Van Diepen, Petrus W.N.; Dilz, Roeland J.; Van Beurden, Martijn C.
17th European Conference on Antennas and Propagation, EuCAP 2023. Institute of Electrical and Electronics Engineers, 2023. blz. 1-5 10133600.

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

TY - GEN

T1 - Jordan Block Eigenvalue Shift in the Marching-on-in-Time Electric Field Integral Equation

AU - Van Diepen, Petrus W.N.

AU - Dilz, Roeland J.

AU - Van Beurden, Martijn C.

PY - 2023/5/31

Y1 - 2023/5/31

N2 - The Marching-on-in-Time Electric Field Integral Equation (MOT-EFIE) and its time differentiated variant (MOT-TDEFIE) both suffer from the linear-in-time instability caused by dimension-two Jordan blocks in the companion-matrix representation. We prove that these Jordan blocks are centered around a specific eigenvalue that depends on the recurrence relation between the interaction matrices. By adapting the recurrence relation, we can move the pertaining eigenvalues of the Jordan blocks to the interior of the unit circle and therefore remove the linear-in-time instability from the scheme. We provide numerical evidence to further illustrate these findings.

AB - The Marching-on-in-Time Electric Field Integral Equation (MOT-EFIE) and its time differentiated variant (MOT-TDEFIE) both suffer from the linear-in-time instability caused by dimension-two Jordan blocks in the companion-matrix representation. We prove that these Jordan blocks are centered around a specific eigenvalue that depends on the recurrence relation between the interaction matrices. By adapting the recurrence relation, we can move the pertaining eigenvalues of the Jordan blocks to the interior of the unit circle and therefore remove the linear-in-time instability from the scheme. We provide numerical evidence to further illustrate these findings.

KW - companion matrix

KW - electric field integral equation

KW - marching-on-in-time

KW - stability

KW - time domain

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U2 - 10.23919/EuCAP57121.2023.10133600

DO - 10.23919/EuCAP57121.2023.10133600

M3 - Conference contribution

AN - SCOPUS:85162190667

SP - 1

EP - 5

BT - 17th European Conference on Antennas and Propagation, EuCAP 2023

PB - Institute of Electrical and Electronics Engineers

T2 - 17th European Conference on Antennas and Propagation, EuCAP 2023

Y2 - 26 March 2023 through 31 March 2023

ER -

Jordan Block Eigenvalue Shift in the Marching-on-in-Time Electric Field Integral Equation

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