Efficient jacobian matrix determination for H2 representations of nonlinear electrostatic surface integral equations

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

doi:10.47037/2020.ACES.J.351101

Efficient jacobian matrix determination for H² representations of nonlinear electrostatic surface integral equations

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

Research output: Contribution to journal › Article › 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
Pages (from-to)	1264-1265
Number of pages	2
Journal	Applied Computational Electromagnetics Society Journal
Volume	35
Issue number	11
DOIs	https://doi.org/10.47037/2020.ACES.J.351101
State	Published - Nov 2020

Bibliographical note

Publisher Copyright:
© ACES.

Funding

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

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

Keywords

Corrosion-related fields
Hierarchical matrices
Nonlinear integral equation
Randomized linear algebra

ASJC Scopus subject areas

Astronomy and Astrophysics
Electrical and Electronic Engineering

Access to Document

10.47037/2020.ACES.J.351101

Cite this

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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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KW - Hierarchical matrices

KW - Nonlinear integral equation

KW - Randomized linear algebra

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