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Your search keyword '"Bernal, Francisco"' showing total 2 results
Start Over Author "Bernal, Francisco" Topic boundary value problems Topic radial basis functions
2 results on '"Bernal, Francisco"'

1. Trust-region methods for nonlinear elliptic equations with radial basis functions.

Author

Bernal, Francisco

Subjects
*NONLINEAR equations, *ELLIPTIC equations, *RADIAL basis functions, *NUMERICAL solutions to differential equations, *BOUNDARY value problems, *COLLOCATION methods
Abstract

We consider the numerical solution of nonlinear elliptic boundary value problems with Kansa’s method. We derive analytic formulas for the Jacobian and Hessian of the resulting nonlinear collocation system and exploit them within the framework of the trust-region algorithm. This ansatz is tested on semilinear, quasilinear and fully nonlinear elliptic PDEs (including Plateau’s problem, Hele–Shaw flow and the Monge–Ampère equation) with excellent results. The new approach distinctly outperforms previous ones based on linearization or finite-difference Jacobians. [ABSTRACT FROM AUTHOR]

Published
2016
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2. On the enriched RBF method for singular potential problems

Author

Bernal, Francisco and Kindelan, Manuel

Subjects
*RADIAL basis functions, *MATHEMATICAL singularities, *NUMERICAL solutions to elliptic differential equations, *BOUNDARY value problems, *OSCILLATIONS, *FINITE element method, *LAPLACIAN operator, *FLUID dynamics
Abstract

Abstract: The performance of Kansa''s method in the solution of elliptic partial differential equations (PDEs) with singular boundary conditions is addressed. Like in all global numerical schemes, low-order singularities bring about Gibbs’ oscillations that deteriorate the accuracy and the convergence rate of Kansa''s method to a great extent. Moreover, they may render it uncapable of handling common problems of incompressible flow. Focussing on a problem of Laplacian flow which is linked to the benchmark Motz problem, it is shown how all these difficulties can be overcome by enriching the radial basis function (RBF) interpolant with the proper singularity-capturing terms. This simple modification even enables Kansa''s method to outperform the finite element method (FEM) in the conservation of Laplacian flow through an irregular channel. [Copyright &y& Elsevier]

Published
2009
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