Convergence of the High-Accuracy Algorithm for Solving the Dirichlet Problem of the Modified Helmholtz Equation

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...

Full description

Bibliographic Details
Main Authors: Hu Li, Guang Zeng
Format: Article
Language:English
Published: Hindawi-Wiley 2020-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2020/6484890
id doaj-e3a3d3c80cf94f11b7f2acb127465369
record_format Article
spelling doaj-e3a3d3c80cf94f11b7f2acb1274653692020-11-24T21:39:51ZengHindawi-WileyComplexity1076-27871099-05262020-01-01202010.1155/2020/64848906484890Convergence 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
collection DOAJ
language English
format Article
sources DOAJ
author Hu Li
Guang Zeng
spellingShingle Hu Li
Guang Zeng
Convergence of the High-Accuracy Algorithm for Solving the Dirichlet Problem of the Modified Helmholtz Equation
Complexity
author_facet Hu Li
Guang Zeng
author_sort Hu Li
title 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_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_sort convergence of the high-accuracy algorithm for solving the dirichlet problem of the modified helmholtz equation
publisher Hindawi-Wiley
series Complexity
issn 1076-2787
1099-0526
publishDate 2020-01-01
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.
url http://dx.doi.org/10.1155/2020/6484890
work_keys_str_mv AT huli convergenceofthehighaccuracyalgorithmforsolvingthedirichletproblemofthemodifiedhelmholtzequation
AT guangzeng convergenceofthehighaccuracyalgorithmforsolvingthedirichletproblemofthemodifiedhelmholtzequation
_version_ 1716682018210709504

Similar Items