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2. G. Beer, J.O. Watson, Introduction to Finite and Boundary Element Methods for Engineers,

By Mr (c: R (n, Peter R. (-tas-cl) Elliott, David (-tas and Reviewed Carsten Carstensen

Abstract

A generalisation of Telles ’ method for evaluating weakly singular boundary element integrals. (English summary) J. Comput. Appl. Math. 131 (2001), no. 1-2, 223–241. For a weakly singular integral with a logarithmic singularity the transformation of the onedimensional contour Γ onto [−1, +1] yields the integral G = ∫ +1 −1 ln |s − s0|ϕ(s)J(s) ds for a given s0, −1 ≤ s0 ≤ 1, and a Jacobian J(s). The proposed method for the evaluation of G consists of a reparametrisation via a bijection γq: [−1, 1] → [−1, 1] with γq(s0) = 0 to compensate for the weak singularity of ln |s − s0|. The resulting nonsingular integrand ln |rq(t) − γq(t0) | ϕ(γq(t))J(γq(t))γ ′ q(t) is then integrated with standard Gauss-Legendre quadrature. The authors suggest the use of the Monegato-Sloan transformation q where γq is a qth degree polynomial. The algorithm generalizes a quadrature technique due to Telles given for q = 3. The truncation error is discussed and numerical examples are included. The proposed algorithm appears very accurate in practise when, e.g., q is chosen as the number of Gauss points

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.363.717
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