Approximate inverse of the rao-wilton-glisson basis functions gram matrix via monopolar representation

Jonas Kornprobst; Josef Knapp; Thomas F. Eibert

doi:10.1109/APUSNCURSINRSM.2019.8888979

Approximate inverse of the rao-wilton-glisson basis functions gram matrix via monopolar representation

Jonas Kornprobst, Josef Knapp, Thomas F. Eibert

Chair of High-Frequency Engineering

Technical University of Munich

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

1 Scopus citations

Abstract

Starting from the monopolar representation of the Rao-Wilton-Glisson (RWG) functions, an approximate inverse (AI) of the RWG Gram matrix is constructed, where only 3x3 matrices for all individual triangles have to be inverted. The inversion of the Gram matrix is, however, only approximate, since it results as the inverse of a product of singular matrices, which is not easily obtained. The AI is shown to be an effective preconditioner for the RWG Gram matrix and is in particular useful for ill-conditioned Gram matrics on distorted meshes.

Original language	English
Title of host publication	2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, APSURSI 2019 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	795-796
Number of pages	2
ISBN (Electronic)	9781728106922
DOIs	https://doi.org/10.1109/APUSNCURSINRSM.2019.8888979
State	Published - Jul 2019
Event	2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, APSURSI 2019 - Atlanta, United States Duration: 7 Jul 2019 → 12 Jul 2019

Publication series

Name	2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, APSURSI 2019 - Proceedings

Conference

Conference	2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, APSURSI 2019
Country/Territory	United States
City	Atlanta
Period	7/07/19 → 12/07/19

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10.1109/APUSNCURSINRSM.2019.8888979

Cite this

Kornprobst, J., Knapp, J., & Eibert, T. F. (2019). Approximate inverse of the rao-wilton-glisson basis functions gram matrix via monopolar representation. In 2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, APSURSI 2019 - Proceedings (pp. 795-796). Article 8888979 (2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, APSURSI 2019 - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/APUSNCURSINRSM.2019.8888979

Kornprobst, Jonas ; Knapp, Josef ; Eibert, Thomas F. / Approximate inverse of the rao-wilton-glisson basis functions gram matrix via monopolar representation. 2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, APSURSI 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 795-796 (2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, APSURSI 2019 - Proceedings).

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abstract = "Starting from the monopolar representation of the Rao-Wilton-Glisson (RWG) functions, an approximate inverse (AI) of the RWG Gram matrix is constructed, where only 3x3 matrices for all individual triangles have to be inverted. The inversion of the Gram matrix is, however, only approximate, since it results as the inverse of a product of singular matrices, which is not easily obtained. The AI is shown to be an effective preconditioner for the RWG Gram matrix and is in particular useful for ill-conditioned Gram matrics on distorted meshes.",

author = "Jonas Kornprobst and Josef Knapp and Eibert, {Thomas F.}",

note = "Publisher Copyright: {\textcopyright} 2019 IEEE.; 2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, APSURSI 2019 ; Conference date: 07-07-2019 Through 12-07-2019",

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series = "2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, APSURSI 2019 - Proceedings",

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Kornprobst, J, Knapp, J & Eibert, TF 2019, Approximate inverse of the rao-wilton-glisson basis functions gram matrix via monopolar representation. in 2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, APSURSI 2019 - Proceedings., 8888979, 2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, APSURSI 2019 - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 795-796, 2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, APSURSI 2019, Atlanta, United States, 7/07/19. https://doi.org/10.1109/APUSNCURSINRSM.2019.8888979

Approximate inverse of the rao-wilton-glisson basis functions gram matrix via monopolar representation. / Kornprobst, Jonas; Knapp, Josef; Eibert, Thomas F.
2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, APSURSI 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. p. 795-796 8888979 (2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, APSURSI 2019 - Proceedings).

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

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N2 - Starting from the monopolar representation of the Rao-Wilton-Glisson (RWG) functions, an approximate inverse (AI) of the RWG Gram matrix is constructed, where only 3x3 matrices for all individual triangles have to be inverted. The inversion of the Gram matrix is, however, only approximate, since it results as the inverse of a product of singular matrices, which is not easily obtained. The AI is shown to be an effective preconditioner for the RWG Gram matrix and is in particular useful for ill-conditioned Gram matrics on distorted meshes.

AB - Starting from the monopolar representation of the Rao-Wilton-Glisson (RWG) functions, an approximate inverse (AI) of the RWG Gram matrix is constructed, where only 3x3 matrices for all individual triangles have to be inverted. The inversion of the Gram matrix is, however, only approximate, since it results as the inverse of a product of singular matrices, which is not easily obtained. The AI is shown to be an effective preconditioner for the RWG Gram matrix and is in particular useful for ill-conditioned Gram matrics on distorted meshes.

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Kornprobst J, Knapp J, Eibert TF. Approximate inverse of the rao-wilton-glisson basis functions gram matrix via monopolar representation. In 2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, APSURSI 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2019. p. 795-796. 8888979. (2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, APSURSI 2019 - Proceedings). doi: 10.1109/APUSNCURSINRSM.2019.8888979

Approximate inverse of the rao-wilton-glisson basis functions gram matrix via monopolar representation

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