Browsing Τμήμα Μαθηματικών και Στατιστικής / Department of Mathematics and Statistics by Subject "Numerical methods"
Now showing items 1-20 of 24
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Article
Conforming Chebyshev spectral methods for Poisson problems in rectangular domains
(1993)Four and six-element conforming domain decomposition techniques are developed for Chebyshev spectral collocation methods for Poisson problems in rectangular domains. The applicability of the methods is demonstrated on ...
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Article
Finite element approximation of convection–diffusion problems using an exponentially graded mesh
(2016)We present the analysis of an h version Finite Element Method for the approximation of the solution to convection–diffusion problems. The method uses piece-wise polynomials of degree p≥1, defined on an exponentially graded ...
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Article
A fully conforming spectral collocation scheme for second- and fourth-order problems
(1995)A spectral element scheme is presented for the solution of second- and fourth-order problems in two and three space dimensions. This scheme is based on a collocation formulation and, for a certain class of problems, results ...
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Article
A Kansa-Radial Basis Function Method for Elliptic Boundary Value Problems in Annular Domains
(2015)We employ a Kansa-radial basis function (RBF) method for the numerical solution of elliptic boundary value problems in annular domains. This discretization leads, with an appropriate selection of collocation points and for ...
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Article
Kansa-RBF algorithms for elliptic problems in axisymmetric domains
(2016)We employ a Kansa-radial basis function method for the numerical solution of elliptic boundary value problems in three-dimensional axisymmetric domains. We consider problems governed by the Poisson equation, the inhomogeneous ...
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Article
A meshless numerical identification of a sound-hard obstacle
(2012)We propose a simple meshless method for detecting a rigid (sound-hard) scatterer embedded in a host acoustic homogeneous medium from scant measurements of the scattered near field. This inverse problem is ill-posed since ...
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Article
The method of fundamental solutions for heat conduction in layered materials
(1999)In this paper, we investigate the application of the Method of Fundamental Solutions (MFS) to two-dimensional problems of steady-state heat conduction in isotropic and anisotropic bimaterials. Two approaches are used: a ...
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Article
The method of fundamental solutions for three-dimensional inverse geometric elasticity problems
(2016)We investigate the numerical reconstruction of smooth star-shaped voids (rigid inclusions and cavities) which are compactly contained in a three-dimensional isotropic linear elastic medium from a single set of Cauchy data ...
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Conference Object
Note on the distribution of extreme wave crests
(2005)The sea elevation at a fixed point is modelled by means of a second order model, which is a smooth algebraic function of a vector valued Gaussian process. Asymptotic methods, presented first in [1], are used to estimate ...
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Article
A numerical conformal mapping method for harmonic mixed boundary value problems
(1996)We describe a simple and versatile technique for the numerical solution of harmonic mixed boundary value problems in simply-connected domains. This technique is based on the theory of Riemann-Hilbert problems, and involves ...
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Article
Numerical investigation of the nonlinear heat diffusion equation with high nonlinearity on the boundary
(2008)A nonlinear heat diffusion problem is considered when the thermal conductivity and heat capacity are nonlinear functions of the temperature. At one of the boundaries a highly nonlinear condition is imposed involving both ...
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Article
Numerical similarity reductions of the (1+3)-dimensional Burgers equation
(2011)We consider the (1+3)-dimensional Burgers equation ut = u xx + uyy + uzz + uux which has considerable interest in mathematical physics. Lie symmetries are used to reduce it to certain ordinary differential equations. We ...
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Article
A numerical study of the SVDMFS solution of inverse boundary value problems in two-dimensional steady-state linear thermoelasticity
(2015)We study the reconstruction of the missing thermal and mechanical data on an inaccessible part of the boundary in the case of two-dimensional linear isotropic thermoelastic materials from overprescribed noisy measurements ...
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Article
On the classification of similarity solutions of a two-dimensional diffusion-advection equation
(2007)We consider the two-dimensional diffusion-advection equation ut = Duyy - frac(d k, d u) ux. We present the classification of Lie symmetries of this equation. For the case k(u) = u2 we give the complete list of similarity ...
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Article
Potential field based geometric modelling using the method of fundamental solutions
(2006)We propose a new geometric modelling method based on the so-called potential field (PF) modelling technique. The harmonic problem associated with this technique is solved numerically using the method of fundamental solutions ...
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Article
A singular function boundary integral method for the laplace equation
(1996)The authors present a new singular function boundary integral method for the numerical solution of problems with singularities which is based on approximation of the solution by the leading terms of the local asymptotic ...
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Article
Solution of the square lid-driven cavity flow of a Bingham plastic using the finite volume method
(2013)We investigate the performance of the finite volume method in solving viscoplastic flows. The creeping square lid-driven cavity flow of a Bingham plastic is chosen as the test case and the constitutive equation is regularised ...
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Conference Object
Solution of viscoplastic flows with the finite volume / multigrid method
(National Technical University of Athens, 2013)We investigate the performance of the finite volume method in solving viscoplastic flows. The square lid-driven cavity flow of a Bingham plastic is chosen as the test case and the constitutive equation is regularised as ...
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Article
Some aspects of the one-dimensional version of the method of fundamental solutions
(2001)The method of fundamental solutions (MFS) is a well-established boundary-type numerical method for the solution of certain two- and three-dimensional elliptic boundary value problems. The basic ideas were introduced by ...
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Article
Special boundary approximation methods for laplace equation problems with boundary singularities- Applications to the motz problem
(2006)We investigate the convergence of special boundary approximation methods (BAMs) used for the solution of Laplace problems with a boundary singularity. In these methods, the solution is approximated in terms of the leading ...