A boundary element method recursive procedure applied to Poisson's problems

This paper describes a simple procedure to increase the accuracy of the boundary element method (BEM) results in Poisson's problems using coarse meshes. Usually, BEM values at internal points are obtained by reusing the boundary integral equation, after having calculated all variables at the no...

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Published in:Engineering analysis with boundary elements Vol. 82; pp. 104 - 110
Main Authors: Ramos, V.E.S., Loeffler, C.F., Mansur, W.J.
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.09.2017
Subjects:
Boundary element method
Poisson's equation
Recursive procedure
Weighted residual method
Poisson's equation
Recursive procedure
Boundary element method
Weighted residual method
ISSN:0955-7997, 1873-197X
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Abstract This paper describes a simple procedure to increase the accuracy of the boundary element method (BEM) results in Poisson's problems using coarse meshes. Usually, BEM values at internal points are obtained by reusing the boundary integral equation, after having calculated all variables at the nodal points on the boundary. Accuracy in results of these internal points is superior to that obtained at boundary nodes and the reason for that can be assigned to a new minimization of residuals performed. Therefore, this idea can be used to improve BEM results by means of choosing new source points on the boundary at positions different from those of the original nodes. Tests carried out with problems governed by Laplace's equation and Navier's equation were successful; thus, this procedure is now applied to Poisson's problems that allow a more comprehensive evaluation of the performance of proposed technique.
AbstractList This paper describes a simple procedure to increase the accuracy of the boundary element method (BEM) results in Poisson's problems using coarse meshes. Usually, BEM values at internal points are obtained by reusing the boundary integral equation, after having calculated all variables at the nodal points on the boundary. Accuracy in results of these internal points is superior to that obtained at boundary nodes and the reason for that can be assigned to a new minimization of residuals performed. Therefore, this idea can be used to improve BEM results by means of choosing new source points on the boundary at positions different from those of the original nodes. Tests carried out with problems governed by Laplace's equation and Navier's equation were successful; thus, this procedure is now applied to Poisson's problems that allow a more comprehensive evaluation of the performance of proposed technique.
Author Loeffler, C.F.
Mansur, W.J.
Ramos, V.E.S.
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10.1016/j.enganabound.2010.05.012
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Keywords Poisson's equation
Recursive procedure
Boundary element method
Weighted residual method
Language English
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SubjectTerms Boundary element method
Poisson's equation
Recursive procedure
Weighted residual method
Title A boundary element method recursive procedure applied to Poisson's problems
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