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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

1 Citation (Scopus)

1 Downloads (Pure)

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.

Original language	English
Title of host publication	17th European Conference on Antennas and Propagation, EuCAP 2023
Publisher	Institute of Electrical and Electronics Engineers
Pages	1-5
Number of pages	5
DOIs	https://doi.org/10.23919/EuCAP57121.2023.10133600
Publication status	Published - 31 May 2023
Event	17th European Conference on Antennas and Propagation, EuCAP 2023 - Florence, Italy Duration: 26 Mar 2023 → 31 Mar 2023

Conference

Conference	17th European Conference on Antennas and Propagation, EuCAP 2023
Country/Territory	Italy
City	Florence
Period	26/03/23 → 31/03/23

Keywords

companion matrix
electric field integral equation
marching-on-in-time
stability
time domain

Access to Document

10.23919/EuCAP57121.2023.10133600

Cite this

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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,

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doi = "10.23919/EuCAP57121.2023.10133600",

language = "English",

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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",

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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, pp. 1-5, 17th European Conference on Antennas and Propagation, EuCAP 2023, Florence, Italy, 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. p. 1-5 10133600.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › 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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DO - 10.23919/EuCAP57121.2023.10133600

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

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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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Keywords

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