Development of the Kansa method for solving seepage problems using a new algorithm for the shape parameter optimization

In this research, the Kansa or Multiquadric method (MQ) has been developed for solving the seepage problems in 2D and 3D arbitrary domains. This research is the first application of this method for seepage analysis in both confined and unconfined porous media. The domain decomposition approach has b...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2019-02, Vol.77 (3), p.815-829
Main Authors: Fallah, Alireza, Jabbari, Ehsan, Babaee, Reza
Format: Article
Language:English
Subjects:
Algorithms
Basis functions
Boundary conditions
Computing time
Domain decomposition methods
Meshless method
Multiquadric
Numerical methods
Parameters
Porous media
Radial basis function
RBF
Seepage
Shape parameter
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Summary:In this research, the Kansa or Multiquadric method (MQ) has been developed for solving the seepage problems in 2D and 3D arbitrary domains. This research is the first application of this method for seepage analysis in both confined and unconfined porous media. The domain decomposition approach has been employed for applying MQ method easily in inhomogeneous and irregular complex geometries and decreasing the computational costs. For determining the optimum shape parameter that affects strongly the accuracy of MQ and other RFB methods, a new scheme that decreases drastically the computational time is introduced. The efficiency of the proposed algorithm has been examined under various radial basis functions, variations of number of interpolating points and points distribution, through a numerical example with analytical solution. Eventually, three examples including different boundary conditions are presented. Comparing results of the examples with other numerical methods indicates that the present approach has high capability and accuracy in solving seepage problems.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2018.10.021