Convergence of the High-Accuracy Algorithm for Solving the Dirichlet Problem of the Modified Helmholtz Equation
In this paper, we derive the convergence for the high-accuracy algorithm in solving the Dirichlet problem of the modified Helmholtz equation. By the boundary element method, we transform the system to be a boundary integral equation. The high-accuracy algorithm using the specific quadrature rule is...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/6484890 |
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| _version_ | 1832567484456108032 |
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| author | Hu Li Guang Zeng |
| author_facet | Hu Li Guang Zeng |
| author_sort | Hu Li |
| collection | DOAJ |
| description | In this paper, we derive the convergence for the high-accuracy algorithm in solving the Dirichlet problem of the modified Helmholtz equation. By the boundary element method, we transform the system to be a boundary integral equation. The high-accuracy algorithm using the specific quadrature rule is developed to deal with weakly singular integrals. The convergence of the algorithm is proved based on Anselone’s collective compact theory. Moreover, an asymptotic error expansion shows that the algorithm is of order Oh03. The numerical examples support the theoretical analysis. |
| format | Article |
| id | doaj-art-e3a3d3c80cf94f11b7f2acb127465369 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-e3a3d3c80cf94f11b7f2acb1274653692025-02-03T01:01:32ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/64848906484890Convergence of the High-Accuracy Algorithm for Solving the Dirichlet Problem of the Modified Helmholtz EquationHu Li0Guang Zeng1School of Mathematics, Chengdu Normal University, Chengdu 611130, ChinaSchool of Sciences, East China University of Technology, Nanchang 330013, ChinaIn this paper, we derive the convergence for the high-accuracy algorithm in solving the Dirichlet problem of the modified Helmholtz equation. By the boundary element method, we transform the system to be a boundary integral equation. The high-accuracy algorithm using the specific quadrature rule is developed to deal with weakly singular integrals. The convergence of the algorithm is proved based on Anselone’s collective compact theory. Moreover, an asymptotic error expansion shows that the algorithm is of order Oh03. The numerical examples support the theoretical analysis.http://dx.doi.org/10.1155/2020/6484890 |
| spellingShingle | Hu Li Guang Zeng Convergence of the High-Accuracy Algorithm for Solving the Dirichlet Problem of the Modified Helmholtz Equation Complexity |
| title | Convergence of the High-Accuracy Algorithm for Solving the Dirichlet Problem of the Modified Helmholtz Equation |
| title_full | Convergence of the High-Accuracy Algorithm for Solving the Dirichlet Problem of the Modified Helmholtz Equation |
| title_fullStr | Convergence of the High-Accuracy Algorithm for Solving the Dirichlet Problem of the Modified Helmholtz Equation |
| title_full_unstemmed | Convergence of the High-Accuracy Algorithm for Solving the Dirichlet Problem of the Modified Helmholtz Equation |
| title_short | Convergence of the High-Accuracy Algorithm for Solving the Dirichlet Problem of the Modified Helmholtz Equation |
| title_sort | convergence of the high accuracy algorithm for solving the dirichlet problem of the modified helmholtz equation |
| url | http://dx.doi.org/10.1155/2020/6484890 |
| work_keys_str_mv | AT huli convergenceofthehighaccuracyalgorithmforsolvingthedirichletproblemofthemodifiedhelmholtzequation AT guangzeng convergenceofthehighaccuracyalgorithmforsolvingthedirichletproblemofthemodifiedhelmholtzequation |