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Desingularization of matrix equations employing hypersingular integrals in boundary element methods using double nodes

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Title: Desingularization of matrix equations employing hypersingular integrals in boundary element methods using double nodes
Authors: Tomioka, Satoshi Browse this author →KAKEN DB
Nishiyama, Shusuke Browse this author
Matsumoto, Yutaka Browse this author →KAKEN DB
Miyamoto, Naoki Browse this author →KAKEN DB
Keywords: Boundary element method
Hypersingular integral
Helmholtz equation
Double node
Boundary condition
Regularization of coefficient matrix
Rank deficiency
Issue Date: Sep-2019
Publisher: Elsevier
Journal Title: Engineering analysis with boundary elements
Volume: 106
Start Page: 493
End Page: 504
Publisher DOI: 10.1016/j.enganabound.2019.06.003
Abstract: In boundary element methods, using double nodes at corners is a useful approach to uniquely define the normal direction of boundary elements. However, matrix equations constructed by conventional boundary integral equations (CBIEs) become singular under certain combinations of double node boundary conditions. In this paper, we analyze the singular conditions of the CBIE formulation for cases where the boundary conditions at the double node are imposed by combinations of Dirichlet, Neumann, Robin, and interface conditions. To address this singularity, we propose the use of hypersingular integral equations (HBIEs) for wave propagation problems that obey the Helmholtz equation. To demonstrate the applicability of HBIE, we compare three types of simultaneous equations: (i) CBIE, (ii) partial-HBIE where the HBIE is only applied to the double nodes at corners while the CBIE is applied to the other nodes, and (iii) full-HBIE where the HBIE is applied to all nodes. Based on our numerical results, we observe the following results. The singularity of the matrix equations for problems with any combination of boundary conditions can be resolved by both full-HBIEs and partial-HBIEs, and the partial-HBIE exhibits better accuracy than the full-HBIE. Furthermore, the computational cost of partial-HBIEs is smaller than that of full-HBIEs.
Rights: © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Type: article (author version)
Appears in Collections:工学院・工学研究院 (Graduate School of Engineering / Faculty of Engineering) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 富岡 智

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