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Identification and reconstruction of a small leak zone in a pipe by a spectral element method
(2006)
This paper deals with the identification of a zone permitting fluid to leak out of a drain. Using the analogy with crack identification by boundary measurements, we give uniqueness and stability results and we propose an ...
Optimal superconvergent one step nodal cubic spline collocation methods
(2006)
We formulate new optimal (fourth) order one step nodal cubic spline collocation methods for the solution of various elliptic boundary value problems in the unit square. These methods are constructed so that the respective ...
A nonoverlapping domain decomposition method for Legendre spectral collocation problems
(2007)
We consider the Dirichlet boundary value problem for Poisson's equation in an L-shaped region or a rectangle with a cross-point. In both cases, we approximate the Dirichlet problem using Legendre spectral collocation, that ...
Local RBF Algorithms for Elliptic Boundary Value Problems in Annular Domains
(2019)
A local radial basis function method (LRBF) is applied for the solution of boundary value problems in annular domains governed by the Poisson equation, the inhomogeneous biharmonic equation and the inhomogeneous Cauchy-Navier ...
Moving pseudo-boundary method of fundamental solutions for nonlinear potential problems
(2019)
In the method of fundamental solutions (MFS), the solution of a boundary value problem (BVP) is approximated by a linear combination of fundamental solutions expressed in terms of sources which are located on a pseudo–boundary ...
Kansa RBF method for nonlinear problems
(2018)
We apply the Kansa–radial basis function (RBF) collocation method to two– dimensional nonlinear boundary value problems. The system of nonlinear equations resulting from the Kansa–RBF discretization is solved by directly ...
The method of fundamental solutions for the Oseen steady-state viscous flow past obstacles of known or unknown shapes
(2019)
In this paper, the steady-state Oseen viscous flow equations past a known or unknown obstacle are solved numerically using the method of fundamental solutions (MFS), which is free of meshes, singularities, and numerical ...
Kansa-RBF algorithms for elliptic problems in regular polygonal domains
(2018)
We propose matrix decomposition algorithms for the efficient solution of the linear systems arising from Kansa radial basis function discretizations of elliptic boundary value problems in regular polygonal domains. These ...
Shape parameter estimation in RBF function approximation
(2019)
The radial basis function (RBF) collocation method is applied for the approximation of functions in two variables. When the RBFs employed include a shape parameter, the determination of an appropriate value for it is a ...
Determination of shape parameter in RBF approximation
(WIT Press, 2019)
We apply a radial basis function (RBF) collocation method for the approximation of functions in two dimensions. The solution is approximated by a linear combination of radial basis functions. The issue of determining the ...