Browsing by Subject "Biharmonic equation"
Now showing items 1-15 of 15
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A conforming spectral technique for biharmonic-type problems in rectangular domains
(1994)A conforming domain decomposition Chebyshev spectral collocation method is developed for the solution of biharmonic-type problems in rectangular domains. Careful selection of the collocation points ensures that the solution ...
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Article
Efficient algorithms for approximating particular solutions of elliptic equations using Chebyshev polynomials
(2007)In this paper, we propose efficient algorithms for approximating particular solutions of second and fourth order elliptic equations. The approximation of the particular solution by a truncated series of Chebyshev polynomials ...
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Article
Efficient MFS algorithms in regular polygonal domains
(2009)In this work, we apply the Method of Fundamental Solutions (MFS) to harmonic and biharmonic problems in regular polygonal domains. The matrices resulting from the MFS discretization possess a block circulant structure. ...
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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
Matrix decomposition algorithms for elliptic boundary value problems: A survey
(2011)We provide an overview of matrix decomposition algorithms (MDAs) for the solution of systems of linear equations arising when various discretization techniques are applied in the numerical solution of certain separable ...
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A matrix decomposition MFS algorithm for axisymmetric biharmonic problems
(2005)We consider the approximate solution of axisymmetric biharmonic problems using a boundary-type meshless method, the Method of Fundamental Solutions (MFS) with fixed singularities and boundary collocation. For such problems, ...
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Article
A matrix decomposition MFS algorithm for biharmonic problems in annular domains
(2004)The Method of Fundamental Solutions (MFS) is a boundary-type method for the solution of certain elliptic boundary value problems. In this work, we develop an efficient matrix decomposition MFS algorithm for the solution ...
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Article
A matrix decomposition MFS algorithm for problems in hollow axisymmetric domains
(2006)In this work we apply the Method of Fundamental Solutions (MFS) with fixed singularities and boundary collocation to certain axisymmetric harmonic and biharmonic problems. By exploiting the block circulant structure of the ...
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Article
The method of fundamental solutions for elliptic problems in circular domains with mixed boundary conditions
(2015)We apply the method of fundamental solutions (MFS) for the solution of harmonic and biharmonic problems in circular domains subject to mixed boundary conditions. In contrast to the cases when boundary conditions of the ...
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Article
On choosing the location of the sources in the MFS
(2016)The satisfactory location for the sources outside the closure of the domain of the problem under consideration remains one of the major issues in the application of the method of fundamental solutions (MFS). In this work ...
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Article
The simple layer potential method of fundamental solutions for certain biharmonic problems
(1989)A novel formulation of the method of fundamental solutions for the numerical solution of plane biharmonic problems, based on the simple layer potential representation of Fichera, is presented. The applicability and accuracy ...
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Article
The singular function boundary integral method for a two-dimensional fracture problem
(2006)The singular function boundary integral method (SFBIM) originally developed for Laplacian problems with boundary singularities is extended for solving two-dimensional fracture problems formulated in terms of the Airy stress ...
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Article
The singular function boundary integral method for biharmonic problems with crack singularities
(2007)We use the singular function boundary integral method (SFBIM) to solve two model fracture problems on the plane. In the SFBIM, the solution is approximated by the leading terms of the local asymptotic solution expansion, ...
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Article
Solution of the planar Newtonian stick-slip problem with the singular function boundary integral method
(2005)A singular function boundary integral method (SFBIM) is proposed for solving biharmonic problems with boundary singularities. The method is applied to the Newtonian stick-slip flow problem. The streamfunction is approximated ...