research-article

An accelerated boundary element method via cross approximation of integral kernels for large‐scale cathodic protection problems

Authors:

Theodore V. Gortsas,

Stephanos V. Tsinopoulos,

Demosthenes PolyzosAuthors Info & Claims

Computer‐Aided Civil and Infrastructure Engineering, Volume 37, Issue 7

Pages 848 - 863

https://doi.org/10.1111/mice.12687

Published: 06 May 2022 Publication History

Abstract

The boundary element method (BEM), combined with hierarchical matrices (HM) and adaptive cross approximation (ACA) techniques, is a powerful tool for treating large‐scale cathodic protection (CP) problems in offshore engineering. Although HM‐ACA/BEM achieves significant memory and time reduction compared to conventional BEM, its application to large‐scale CP problems remains time consuming. In this work, a new, more efficient HM‐ACA/BEM is proposed. The linear system coefficient matrix, obtained by BEM, is partitioned hierarchically into admissible and nonadmissible submatrices. The low‐rank approximation of the admissible submatrices is accomplished indirectly, via a hybrid approach, utilizing approximations of the fundamental solutions and performing only a small number of integrations. The approximation of the fundamental solutions is obtained by a novel, two‐step procedure, which uses a small number of Lebedev points. The proposed methodology is general and integral kernel independent, and thus can be applied to all differential equations solved by BEM. The efficiency of the proposed method is demonstrated by solving a large‐scale CP problem dealing with the protection of an oil–steel offshore platform by sacrificial anodes.

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Cited By

Jiao PYe XZhang CLi WWang H(2024)Vision‐based real‐time marine and offshore structural health monitoring system using underwater robotsComputer-Aided Civil and Infrastructure Engineering10.1111/mice.1299339:2(281-299)Online publication date: 8-Jan-2024
https://dl.acm.org/doi/10.1111/mice.12993
Li XHuang YZhou YWang XZhao DChen C(2023)Predicting the life cycle durability and ecological performance of cementitious coatings with a fuzzy‐stochastics–based approachComputer-Aided Civil and Infrastructure Engineering10.1111/mice.1304839:7(983-1002)Online publication date: 23-May-2023
https://dl.acm.org/doi/10.1111/mice.13048

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An accelerated boundary element method via cross approximation of integral kernels for large‐scale cathodic protection problems

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cover image Computer-Aided Civil and Infrastructure Engineering

Computer-Aided Civil and Infrastructure Engineering Volume 37, Issue 7

June 2022

130 pages

ISSN:1093-9687

EISSN:1467-8667

DOI:10.1111/mice.v37.7

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© 2021 Computer‐Aided Civil and Infrastructure Engineering.

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John Wiley & Sons, Inc.

United States

Publication History

Published: 06 May 2022

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Cited By

Jiao PYe XZhang CLi WWang H(2024)Vision‐based real‐time marine and offshore structural health monitoring system using underwater robotsComputer-Aided Civil and Infrastructure Engineering10.1111/mice.1299339:2(281-299)Online publication date: 8-Jan-2024
https://dl.acm.org/doi/10.1111/mice.12993
Li XHuang YZhou YWang XZhao DChen C(2023)Predicting the life cycle durability and ecological performance of cementitious coatings with a fuzzy‐stochastics–based approachComputer-Aided Civil and Infrastructure Engineering10.1111/mice.1304839:7(983-1002)Online publication date: 23-May-2023
https://dl.acm.org/doi/10.1111/mice.13048

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