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  • 1
    Electronic Resource
    Electronic Resource
    Méthodes spectrales dans une portion de disque (1996)
    Springer
    Numerische Mathematik 73 (1996), S. 265-289 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):65N35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Summary. This paper is devoted to spectral methods for the discretization of elliptic equations in a part of a disk, relying on the use of polar coordinates and approximation by high degree polynomials with respect to each coordinate. We describe the discretization for two model problems: the Poisson equation and the bilaplacian equation, we perform the numerical analysis in each case and we present numerical results.
    Notes: Résumé. On propose une méthode spectrale pour la discrétisation d'équations elliptiques dans une portion de disque, par passage en coordonnées polaires et approximation par des polynômes de degréélevé par rapport à chaque coordonnée. On décrit la discrétisation pour deux problèmes modèle: l'équation de Poisson et l'équation du bilaplacien, on en effectue l'analyse et on présente des résultats numériques.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050193
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  • 2
    Electronic Resource
    Electronic Resource
    Conforming Chebyshev spectral methods for Poisson problems in rectangular domains (1993)
    Springer
    Journal of scientific computing 8 (1993), S. 123-133 
    Details
    ISSN: 1573-7691
    Keywords: Spectral methods ; Collocation ; Chebyshev polynomials
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract 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 standard test problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01060868
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  • 3
    Electronic Resource
    Electronic Resource
    Conforming spectral methods for Poisson problems in cuboidal domains (1994)
    Springer
    Journal of scientific computing 9 (1994), S. 341-350 
    Details
    ISSN: 1573-7691
    Keywords: Spectral methods ; collocation ; Poisson equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract A Chebyshev collocation strategy is introduced for the subdivision of cuboids into cuboidal subdomains (elements). These elements are conforming, which means that the approximation to the solution isC 0 continuous at all points across their interfaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01575037
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  • 4
    Electronic Resource
    Electronic Resource
    The method of fundamental solutions for elliptic boundary value problems (1998)
    Springer
    Advances in computational mathematics 9 (1998), S. 69-95 
    Details
    ISSN: 1572-9044
    Keywords: elliptic boundary value problems ; fundamental solutions ; nonlinear least squares ; boundary collocation ; 65N38 ; 65N99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The aim of this paper is to describe the development of the method of fundamental solutions (MFS) and related methods over the last three decades. Several applications of MFS-type methods are presented. Techniques by which such methods are extended to certain classes of non-trivial problems and adapted for the solution of inhomogeneous problems are also outlined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018981221740
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  • 5
    Electronic Resource
    Electronic Resource
    Conditioning of Pseudospectral Matrices for Certain Domain Decompositions (1999)
    Springer
    Journal of scientific computing 14 (1999), S. 107-119 
    Details
    ISSN: 1573-7691
    Keywords: Spectral methods ; collocation ; domain decomposition ; conditioning
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract In this paper we examine the conditioning of the matrices resulting from certain conforming pseudospectral approximations. In particular, we consider non-conforming domain decompositions in rectangular domains and the solution of fourth order problems. We investigate the way in which the poor conditioning of these matrices affects the performance, in terms of accuracy, of various direct methods of solution of the resulting systems. We also show how a simple iterative refinement procedure can improve the accuracy of the results obtained with a capacitance technique.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1025676806232
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  • 6
    Electronic Resource
    Electronic Resource
    A note on the satisfaction of the boundary conditions for Chebyshev collocation methods in rectangular domains (1991)
    Springer
    Journal of scientific computing 6 (1991), S. 21-26 
    Details
    ISSN: 1573-7691
    Keywords: Boundary conditions ; Chebyshev ; collocation methods ; boundary value problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract The way boundary conditions are imposed when applying Chebyshev collocation methods to Poisson and biharmonic-type problems in rectangular domains is investigated. It is shown that careful selection of the number of collocation points leads to a linear system ofn linearly independent equations inn unknowns.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01068122
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  • 7
    Electronic Resource
    Electronic Resource
    An efficient direct method for fully conforming spectral collocation schemes (1996)
    Springer
    Numerical algorithms 12 (1996), S. 309-319 
    Details
    ISSN: 1572-9265
    Keywords: Domain decomposition ; spectral collocation ; capacitance techniques ; high performance computing ; 65N35 ; 65F05 ; 65N22
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract An efficient direct method is presented for the solution of the linear systems arising in the solution of second and fourth order problems by certain multidomain spectral collocation schemes. In it, the block structure of the global matrix is exploited. The performance of the method is examined for problems in two and three dimensions on an RS6000 workstation and a Cray J-916 supercomputer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02142810
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  • 8
    Electronic Resource
    Electronic Resource
    The simple layer potential method of fundamental solutions for certain biharmonic problems (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1221-1234 
    Details
    ISSN: 0271-2091
    Keywords: Biharmonic equation ; Stokes flow ; Simple layer potential ; Method of fundamental solutions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: 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 of the method are demonstrated by examining its performance on a set of practical problems arising in Stokes fluid flow.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650091005
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  • 9
    Electronic Resource
    Electronic Resource
    Numerical solution of a free surface problem by a boundary element method (1988)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 91-96 
    Details
    ISSN: 0271-2091
    Keywords: Boundary elements ; Free surface ; Riabouchinsky cavity flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper describes a method for the numerical solution of a Riabouchinsky cavity flow. Application of a boundary element method leads to a system of non-linear equations. The mild singularity appearing at the separation point is treated with the introduction of a curved boundary element, which satisfies the exact behaviour of the free boundary in that neighbourhood.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650080108
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  • 10
    Electronic Resource
    Electronic Resource
    The Almansi method of fundamental solutions for solving biharmonic problems (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1665-1682 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new fundamental solutions method for the numerical solution of two-dimensional biharmonic problems is described. In this method, which is based on the Almansi representation of a biharmonic function in the plane, the approximate solution is expressed in terms of fundamental solutions of Laplace's equation, and is determined by a least squares fit of the boundary conditions. The results of numerical experiments which demonstrate the efficacy of the method are presented.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260714
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