Multilevel augmentation methods for nonlinear boundary integral equations II: Accelerated quadratures and Newton iterations
type: Item
instance of: scholarly article
title: Multilevel augmentation methods for nonlinear boundary integral equations II: Accelerated quadratures and Newton iterations
zbMATH Open document ID: 1271.65145
DOI: 10.1216/JIE-2012-24-4-545
author: Xiangling Chen
author: Zhongying Chen
author: Bin Wu
author: Yuesheng Xu
published in: Journal of Integral Equations and Applications
publication date: 2013-03-14T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.jiea/1362669521
review text: The authors improve their multilevel augmentation method (MAM) previously analyzed in Part I [SIAM J. Numer. Anal. 49, No. 6, 2231--2255 (2011; Zbl 1236.65147)]. They use a product integration scheme in order to accurately evaluate the singular integrals involved in the matrices of MAM. Then, they introduce an efficient approximation technique in implementing the usual Newton scheme which avoids repeated computation in Jacobian matrices. Some numerical experiments are carried out in order to underline the accuracy as well as the efficiency of the modified MAM.
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 65Y20
Mathematics Subject Classification ID: 65N12
zbMATH DE Number: 6144973
zbMATH Keywords: multilevel augmentation method
zbMATH Keywords: nonlinear boundary integral equations
zbMATH Keywords: singular integrals
zbMATH Keywords: integration schemes
zbMATH Keywords: modified Newton iterations
zbMATH Keywords: optimal convergence order
zbMATH Keywords: computational efficiency
zbMATH Keywords: numerical experiments
reviewed by: Calin Ioan Gheorghiu
MaRDI profile type: Publication
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OpenAlex ID: W2061486861
description: scientific article; zbMATH DE number 6144973