An Improved Collocation Meshless Method Based on the Variable Shaped Radial Basis Function for the Solution of the Interior Acoustic Problems
Joint Authors
Wang, Shuang
Li, Shande
Huang, Qibai
Li, Kun
Source
Mathematical Problems in Engineering
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-20, 20 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-10-17
Country of Publication
Egypt
No. of Pages
20
Main Subjects
Abstract EN
As an efficient tool, radial basis function (RBF) has been widely used for the multivariate approximation, interpolating continuous, and the solution of the particle differential equations.
However, ill-conditioned interpolation matrix may be encountered when the interpolation points are very dense or irregularly arranged.
To avert this problem, RBFs with variable shape parameters are introduced, and several new variation strategies are proposed.
Comparison with the RBF with constant shape parameters are made, and the results show that the condition number of the interpolation matrix grows much slower with our strategies.
As an application, an improved collocation meshless method is formulated by employing the new RBF.
In addition, the Hermite-type interpolation is implemented to handle the Neumann boundary conditions and an additional sine/cosine basis is introduced for the Helmlholtz equation.
Then, two interior acoustic problems are solved with the presented method; the results demonstrate the robustness and effectiveness of the method.
American Psychological Association (APA)
Wang, Shuang& Li, Shande& Huang, Qibai& Li, Kun. 2012. An Improved Collocation Meshless Method Based on the Variable Shaped Radial Basis Function for the Solution of the Interior Acoustic Problems. Mathematical Problems in Engineering،Vol. 2012, no. 2012, pp.1-20.
https://search.emarefa.net/detail/BIM-1001786
Modern Language Association (MLA)
Wang, Shuang…[et al.]. An Improved Collocation Meshless Method Based on the Variable Shaped Radial Basis Function for the Solution of the Interior Acoustic Problems. Mathematical Problems in Engineering No. 2012 (2012), pp.1-20.
https://search.emarefa.net/detail/BIM-1001786
American Medical Association (AMA)
Wang, Shuang& Li, Shande& Huang, Qibai& Li, Kun. An Improved Collocation Meshless Method Based on the Variable Shaped Radial Basis Function for the Solution of the Interior Acoustic Problems. Mathematical Problems in Engineering. 2012. Vol. 2012, no. 2012, pp.1-20.
https://search.emarefa.net/detail/BIM-1001786
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1001786