Efficient Jacobian Matrix Determination for H2Representations of Nonlinear Electrostatic Surface Integral Equations

John C. Young; Robert J. Adams; Stephen D. Gedney

doi:10.23919/ACES49320.2020.9196119

Efficient Jacobian Matrix Determination for H₂Representations of Nonlinear Electrostatic Surface Integral Equations

John C. Young
, Robert J. Adams
, Stephen D. Gedney

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

Abstract

In this paper, a nonlinear electrostatic surface integral equation is presented that is suitable for predicting corrosion-related fields. Nonlinear behavior arises due to electrochemical reactions at polarized surfaces. Hierarchical H2 matrices are used to compress the discretized integral equation for the fast solution of large problems. A technique based on randomized linear algebra is discussed for the efficient computation of the Jacobian matrix required at each iteration of a nonlinear solution.

Original language	English
Title of host publication	2020 International Applied Computational Electromagnetics Society Symposium, ACES-Monterey 2020
ISBN (Electronic)	9781733509602
DOIs	https://doi.org/10.23919/ACES49320.2020.9196119
State	Published - Jul 2020
Event	2020 International Applied Computational Electromagnetics Society Symposium, ACES-Monterey 2020 - Virtual, Monterey, United States Duration: Jul 27 2020 → Jul 31 2020

Publication series

Name	2020 International Applied Computational Electromagnetics Society Symposium, ACES-Monterey 2020

Conference

Conference	2020 International Applied Computational Electromagnetics Society Symposium, ACES-Monterey 2020
Country/Territory	United States
City	Virtual, Monterey
Period	7/27/20 → 7/31/20

Bibliographical note

Publisher Copyright:
© 2020 Applied Computational Electromagnetics Society (ACES).

Funding

This work was supported in part by Office of Naval Research Grant N00014-16-1-3066.

Funders	Funder number
Office of Naval Research	N00014-16-1-3066

Keywords

corrosion-related fields
hierarchical matrices
nonlinear integral equation
randomized linear algebra

ASJC Scopus subject areas

Radiation
Computer Networks and Communications
Electrical and Electronic Engineering
Parasitology
Instrumentation

Access to Document

10.23919/ACES49320.2020.9196119

Cite this

Young, J. C., Adams, R. J., & Gedney, S. D. (2020). Efficient Jacobian Matrix Determination for H₂Representations of Nonlinear Electrostatic Surface Integral Equations. In 2020 International Applied Computational Electromagnetics Society Symposium, ACES-Monterey 2020 Article 9196119 (2020 International Applied Computational Electromagnetics Society Symposium, ACES-Monterey 2020). https://doi.org/10.23919/ACES49320.2020.9196119

Young, John C. ; Adams, Robert J. ; Gedney, Stephen D. / Efficient Jacobian Matrix Determination for H₂Representations of Nonlinear Electrostatic Surface Integral Equations. 2020 International Applied Computational Electromagnetics Society Symposium, ACES-Monterey 2020. 2020. (2020 International Applied Computational Electromagnetics Society Symposium, ACES-Monterey 2020).

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abstract = "In this paper, a nonlinear electrostatic surface integral equation is presented that is suitable for predicting corrosion-related fields. Nonlinear behavior arises due to electrochemical reactions at polarized surfaces. Hierarchical H2 matrices are used to compress the discretized integral equation for the fast solution of large problems. A technique based on randomized linear algebra is discussed for the efficient computation of the Jacobian matrix required at each iteration of a nonlinear solution.",

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Young, JC , Adams, RJ & Gedney, SD 2020, Efficient Jacobian Matrix Determination for H₂Representations of Nonlinear Electrostatic Surface Integral Equations. in 2020 International Applied Computational Electromagnetics Society Symposium, ACES-Monterey 2020., 9196119, 2020 International Applied Computational Electromagnetics Society Symposium, ACES-Monterey 2020, 2020 International Applied Computational Electromagnetics Society Symposium, ACES-Monterey 2020, Virtual, Monterey, United States, 7/27/20. https://doi.org/10.23919/ACES49320.2020.9196119

Efficient Jacobian Matrix Determination for H₂Representations of Nonlinear Electrostatic Surface Integral Equations. / Young, John C.; Adams, Robert J.; Gedney, Stephen D.
2020 International Applied Computational Electromagnetics Society Symposium, ACES-Monterey 2020. 2020. 9196119 (2020 International Applied Computational Electromagnetics Society Symposium, ACES-Monterey 2020).

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

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Young JC , Adams RJ, Gedney SD. Efficient Jacobian Matrix Determination for H₂Representations of Nonlinear Electrostatic Surface Integral Equations. In 2020 International Applied Computational Electromagnetics Society Symposium, ACES-Monterey 2020. 2020. 9196119. (2020 International Applied Computational Electromagnetics Society Symposium, ACES-Monterey 2020). doi: 10.23919/ACES49320.2020.9196119