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  • Hadamard finite-part integrals  (1)
  • Numerical Methods and Modeling  (1)
  • boundary integral equations  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Boundary integral equations for the scattering of elastic waves by elastic inclusions with thin interface layers (1992)
    Springer
    Journal of nondestructive evaluation 11 (1992), S. 167-174 
    Details
    ISSN: 1573-4862
    Keywords: Elastic waves ; interface layers ; inclusions ; boundary integral equations ; uniqueness
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract Elastic waves are scattered by an elastic inclusion. The interface between the inclusion and the surrounding material is imperfect: the displacement and traction vectors on one side of the interface are assumed to be linearly related to both the displacement vector and the traction vector on the other side of the interface. The literature on such inclusion problems is reviewed, with special emphasis on the development of interface conditions modeling different types of interface layer. Inclusion problems are formulated mathematically, and uniqueness theorems are proved. Finally, various systems of boundary integral equations over the interface are derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00566407
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    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    HYPERSINGULAR INTEGRALS: HOW SMOOTH MUST THE DENSITY BE? (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 687-704 
    Details
    ISSN: 0029-5981
    Keywords: boundary element methods ; Cauchy principal-value integrals ; Hadamard finite-part integrals ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Hypersingular integrals are guaranteed to exist at a point x only if the density function f in the integrand satisfies certain conditions in a neighbourhood of x. It is well known that a sufficient condition is that f has a Hölder-continuous first derivative. This is a stringent condition, especially when it is incorporated into boundary-element methods for solving hypersingular integral equations. This paper is concerned with finding weaker conditions for the existence of one-dimensional Hadamard finite-part integrals: it is shown that it is sufficient for the even part of f (with respect to x) to have a Hölder-continuous first derivative - the odd part is allowed to be discontinuous. A similar condition is obtained for Cauchy principal-value integrals. These simple results have non-trivial consequences. They are applied to the calculation of the tangential derivative of a single-layer potential and to the normal derivative of a double-layer potential. Particular attention is paid to discontinuous densities and to discontinuous boundary conditions. Also, despite the weaker sufficient conditions, it is reaffirmed that, for hypersingular integral equations, collocation at a point x at the junction between two standard conforming boundary elements is not permissible, theoretically. Various modifications to the definition of finite-part integral are explored.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 3
    Electronic Resource
    Electronic Resource
    Smoothness-relaxation strategies for singular and hypersingular integral equations (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 885-906 
    Details
    ISSN: 0029-5981
    Keywords: boundary elements ; Cauchy principal-value integrals ; Hadamard finite part integrals ; Hölder continuity ; relaxed regularization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Three stages are involved in the formulation of a typical direct boundary element method: derivation of an integral representation; taking a Limit To the Boundary (LTB) so as to obtain an integral equation; and discretization. We examine the second and third stages, focussing on strategies that are intended to permit the relaxation of standard smoothness assumptions. Two such strategies are indicated. The first is the introduction of various apparent or ‘pseudo-LTBs’. The second is ‘relaxed regularization’, in which a regularized integral equation, derived rigorously under certain smoothness assumptions, is used when less smoothness is available. Both strategies are shown to be based on inconsistent reasoning. Nevertheless, reasons are offered for having some confidence in numerical results obtained with certain strategies. Our work is done in two physical contexts, namely two-dimensional potential theory (using functions of a complex variable) and three-dimensional elastostatics. © 1998 John Wiley & Sons, Ltd.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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