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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 ...
Matrix decomposition algorithms for modified spline collocation for Helmholtz problems
(2003)
We consider the solution of various boundary value problems for the Helmholtz equation in the unit square using a nodal cubic spline collocation method and modifications of it which produce optimal (fourth-) order ...
A Legendre spectral Galerkin method for the biharmonic Dirichlet problem
(2001)
A Legendre spectral Galerkin method is presented for the solution of the biharmonic Dirichlet problem on a square. The solution and its Laplacian are approximated using the set of basis functions suggested by Shen, which ...
Stress intensity factor computation using the method of fundamental solutions: Mixed-mode problems
(2007)
The method of fundamental solutions is applied to the computation of stress intensity factors in linear elastic fracture mechanics. The displacements are approximated by linear combinations of the fundamental solutions of ...
A spectral mortar element discretization of the Poisson equation with mixed boundary conditions
(2007)
In this paper, we study a spectral mortar element discretization of the Poisson equation on a square subject to mixed boundary conditions of Dirichlet and Neumann type. We carry out the numerical analysis of the method and ...
High performance solution of partial differential equations discretized using a chebyshev spectral collocation method
(1996)
When a Chebyshev spectral collocation method is applied to a flow problem in a rectangularly decomposable domain it leads to the solution of a structured linear system. Since the linear system is solved at each step of a ...
Efficient MFS algorithms for problems in thermoelasticity
(2013)
We propose efficient fast Fourier transform (FFT)-based algorithms using the method of fundamental solutions (MFS) for the numerical solution of certain problems in planar thermoelasticity. In particular, we consider ...
Matrix decomposition MFS algorithms for elasticity and thermo-elasticity problems in axisymmetric domains
(2007)
In this work, we propose an efficient matrix decomposition algorithm for the Method of Fundamental Solutions when applied to three-dimensional boundary value problems governed by elliptic systems of partial differential ...
Matrix decomposition MFS algorithms
(2006)
We describe the application of the Method of Fundamental Solutions (MFS) to elliptic boundary value problems in rotationally symmetric problems. In particular, we show how efficient matrix decomposition MFS algorithms can ...