A Direct Method for Solving Singular Integrals in Three-Dimensional Time-Domain Boundary Element Method for Elastodynamics
The analytically time integrable time-space domain (ATI-TSD) is discovered based on which the minimum time-space domain is identified for treatment on singularities in the three-dimensional time-domain boundary element method (3D TD-BEM) formulation. A direct method to solve singular integrals in th...
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MDPI AG
2022-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/2/286 |
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| author | Xiaofei Qin Youhua Fan Hongjun Li Weidong Lei |
| author_facet | Xiaofei Qin Youhua Fan Hongjun Li Weidong Lei |
| author_sort | Xiaofei Qin |
| collection | DOAJ |
| description | The analytically time integrable time-space domain (ATI-TSD) is discovered based on which the minimum time-space domain is identified for treatment on singularities in the three-dimensional time-domain boundary element method (3D TD-BEM) formulation. A direct method to solve singular integrals in the 3D TD-BEM formulation for elastodynamic problems is proposed. The wavefront singularity can be analytically eliminated in ATI-TSD, while the dual singularity can be treated by the direct method using Kutt’s quadrature in the identified minimum time-space domain. Three benchmark examples are presented to verify the correctness and the applicability of the direct method for solving the singular integrals in 3D TD-BEM. |
| first_indexed | 2024-03-10T01:01:07Z |
| format | Article |
| id | doaj.art-f057d38d26cc459a9df47cb07a7cc9ff |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T01:01:07Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-f057d38d26cc459a9df47cb07a7cc9ff2023-11-23T14:35:14ZengMDPI AGMathematics2227-73902022-01-0110228610.3390/math10020286A Direct Method for Solving Singular Integrals in Three-Dimensional Time-Domain Boundary Element Method for ElastodynamicsXiaofei Qin0Youhua Fan1Hongjun Li2Weidong Lei3School of Science, Harbin Institute of Technology, Shenzhen 518055, ChinaSchool of Science, Harbin Institute of Technology, Shenzhen 518055, ChinaUrban and Rural Construction Institute, Hebei Agricultural University, Baoding 071001, ChinaSchool of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen 518055, ChinaThe analytically time integrable time-space domain (ATI-TSD) is discovered based on which the minimum time-space domain is identified for treatment on singularities in the three-dimensional time-domain boundary element method (3D TD-BEM) formulation. A direct method to solve singular integrals in the 3D TD-BEM formulation for elastodynamic problems is proposed. The wavefront singularity can be analytically eliminated in ATI-TSD, while the dual singularity can be treated by the direct method using Kutt’s quadrature in the identified minimum time-space domain. Three benchmark examples are presented to verify the correctness and the applicability of the direct method for solving the singular integrals in 3D TD-BEM.https://www.mdpi.com/2227-7390/10/2/286time-space coordinate systemtime domain boundary element method (TD-BEM)Kutt’s quadraturetime-space integration domainsingular integrals |
| spellingShingle | Xiaofei Qin Youhua Fan Hongjun Li Weidong Lei A Direct Method for Solving Singular Integrals in Three-Dimensional Time-Domain Boundary Element Method for Elastodynamics Mathematics time-space coordinate system time domain boundary element method (TD-BEM) Kutt’s quadrature time-space integration domain singular integrals |
| title | A Direct Method for Solving Singular Integrals in Three-Dimensional Time-Domain Boundary Element Method for Elastodynamics |
| title_full | A Direct Method for Solving Singular Integrals in Three-Dimensional Time-Domain Boundary Element Method for Elastodynamics |
| title_fullStr | A Direct Method for Solving Singular Integrals in Three-Dimensional Time-Domain Boundary Element Method for Elastodynamics |
| title_full_unstemmed | A Direct Method for Solving Singular Integrals in Three-Dimensional Time-Domain Boundary Element Method for Elastodynamics |
| title_short | A Direct Method for Solving Singular Integrals in Three-Dimensional Time-Domain Boundary Element Method for Elastodynamics |
| title_sort | direct method for solving singular integrals in three dimensional time domain boundary element method for elastodynamics |
| topic | time-space coordinate system time domain boundary element method (TD-BEM) Kutt’s quadrature time-space integration domain singular integrals |
| url | https://www.mdpi.com/2227-7390/10/2/286 |
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