Forward and inverse problems in piezoelectricity using isogeometric symmetric Galerkin boundary element method and level set method

authored by: B. H. Nguyen, Srivilliputtur Subbiah Nanthakumar, Y. Q. He, H. D. Tran, K. Hackl, Xiaoying Zhuang
Abstract: This work presents the method to combine isogeometric analysis coupled to symmetric Galerkin boundary element method (IGA-SGBEM) and parametric level set (PaLS)-based optimization scheme for the analysis of linear problems in two-dimensional piezoelectric media. IGA-SGBEM is used to obtain field variables (i.e. generalized displacement and traction) in the forward analysis. Then, inverse analysis of flaw detection in piezoelectric structures is attempted by combining IGA-SGBEM with PaLS-based optimization scheme. In this proposed method, the versatility of isogeometric analysis (IGA) is proved in the inverse progress, where the iso-line of the level set function can be easily reconstructed and incorporated into the IGA framework. Numerical examples are examined to validate and to demonstrate the robustness of the proposed method in solving both forward and inverse problems in piezoelectricity.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Dalian University of Technology
University of Utah
Ruhr-Universität Bochum
Ton Duc Thang University
Tongji University
Type: Article
Journal: Engineering Analysis with Boundary Elements
Volume: 113
Pages: 118-132
No. of pages: 15
ISSN: 0955-7997
Publication date: 04.2020
Publication status: Published
ASJC Scopus subject areas: General Engineering, Computational Mathematics, Analysis, Applied Mathematics
Electronic version(s): https://doi.org/10.1016/j.enganabound.2019.12.020 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{2e673f79be424b3e9ca7ebd5b75a19fa,
title = "Forward and inverse problems in piezoelectricity using isogeometric symmetric Galerkin boundary element method and level set method",
abstract = "This work presents the method to combine isogeometric analysis coupled to symmetric Galerkin boundary element method (IGA-SGBEM) and parametric level set (PaLS)-based optimization scheme for the analysis of linear problems in two-dimensional piezoelectric media. IGA-SGBEM is used to obtain field variables (i.e. generalized displacement and traction) in the forward analysis. Then, inverse analysis of flaw detection in piezoelectric structures is attempted by combining IGA-SGBEM with PaLS-based optimization scheme. In this proposed method, the versatility of isogeometric analysis (IGA) is proved in the inverse progress, where the iso-line of the level set function can be easily reconstructed and incorporated into the IGA framework. Numerical examples are examined to validate and to demonstrate the robustness of the proposed method in solving both forward and inverse problems in piezoelectricity.",
keywords = "Inverse problem, Isogeometric analysis, Level set method, Piezoelectric material, Symmetric Galerkin BEM",
author = "Nguyen, {B. H.} and Nanthakumar, {Srivilliputtur Subbiah} and He, {Y. Q.} and Tran, {H. D.} and K. Hackl and Xiaoying Zhuang",
note = "Funding Information: B.H. Nguyen, S.S. Nanthakumar and X. Zhuang acknowledge the support from ERC Starting Grant (802205). Appendix A ",
year = "2020",
month = apr,
doi = "10.1016/j.enganabound.2019.12.020",
language = "English",
volume = "113",
pages = "118--132",
journal = "Engineering Analysis with Boundary Elements",
issn = "0955-7997",
publisher = "Elsevier Ltd.",
}