A localized RBF-MLPG method and its application to elliptic PDEs View Full Text


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Article Info

DATE

2019-02-07

AUTHORS

Mansour Safarpoor, Fariba Takhtabnoos, Ahmad Shirzadi

ABSTRACT

The existing local RBF methods use the strong form equation and approximate the solution in local subdomains instead of the whole domain. In the RBF-MLPG method, the unknown solution is approximated by RBFs in the whole domain and testing is done by constructing the weak-form equations over the local subdomains. This paper proposes to approximate the unknown solution locally in the RBF-MLPG method, i.e., in the localized RBF-MLPG method, both solution approximation and testing are treated locally. As a result, the final global matrix becomes sparser and more accurate solutions can be obtained. The method is applied for the numerical solution of elliptic PDEs. The comparison of the results demonstrates the effectiveness of the method. More... »

PAGES

1-13

References to SciGraph publications

  • 2017-10. The numerical solution of two-dimensional logarithmic integral equations on normal domains using radial basis functions with polynomial precision in ENGINEERING WITH COMPUTERS
  • 2019-01. Application of dual-Chebyshev wavelets for the numerical solution of boundary integral equations with logarithmic singular kernels in ENGINEERING WITH COMPUTERS
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  • 2014-02. Solving heat conduction problems by the Direct Meshless Local Petrov-Galerkin (DMLPG) method in NUMERICAL ALGORITHMS
  • 2017-10. Numerical investigation based on direct meshless local Petrov Galerkin (direct MLPG) method for solving generalized Zakharov system in one and two dimensions and generalized Gross–Pitaevskii equation in ENGINEERING WITH COMPUTERS
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