Use of singularity capturing functions in the solution of problems with discontinuous boundary conditions

A method is proposed to improve the accuracy of the numerical solution of elliptic problems with discontinuous boundary conditions using both global and local meshless collocation methods with multiquadrics as basis functions. It is based on the use of special functions which capture the singular be...

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Bibliographic Details
Published in:Engineering analysis with boundary elements 2009-02, Vol.33 (2), p.200-208
Main Authors: Bernal, F., Gutierrez, G., Kindelan, M.
Format: Article
Language:English
Subjects:
Accuracy
Analytical and numerical techniques
Basis functions
Boundary conditions
Boundary-integral methods
Collocation
Computational techniques
Discontinuous boundary conditions
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
General theory
Heat transfer
Laminar flows
Laminar flows in cavities
Mathematical analysis
Mathematical methods in physics
Mathematical models
Meshless methods
Physics
Radial basis function
Singularities
Stokes problem
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Summary:A method is proposed to improve the accuracy of the numerical solution of elliptic problems with discontinuous boundary conditions using both global and local meshless collocation methods with multiquadrics as basis functions. It is based on the use of special functions which capture the singular behavior near discontinuities in boundary conditions. In the case of global collocation, the method consists in enlarging the functional space spanned by the RBF basis functions, while in the case of local collocation, the method consists in modifying appropriately the problem in order to eliminate the singularities from the formulation. Numerical results for benchmark problems such as a stationary heat equation in a box (harmonic) and Stokes flow in a lid-driven square cavity, show significant improvements in accuracy and in compliance with the continuity equation.
ISSN:0955-7997
1873-197X
DOI:10.1016/j.enganabound.2008.05.002