WIT Press


Automatic Differentiation For The Evaluation Of Singular Integrals In Two-dimensional Boundary Element Computations

Price

Free (open access)

Paper DOI

10.2495/BE970661

Volume

19

Pages

10

Published

1997

Size

713 kb

Author(s)

D. Crann, D.B. Christiansen, A.J. Davies and S.A. Brown

Abstract

In the evaluation of the logarithmic singular integrals which arise in two-dimensional boundary element computations a variety of approaches may be adopted. For linear elements the integrals may be performed analytically. For quadratic elements an approximate method is required and the most common technique is to use a special logarithmic numerical quadrature. A second approach uses a transformation in such a way that the Jacobian is zero at the singular point removing the singularity, conventional Gauss quadrature may then be used. A third possibility is to expand the Jacobian as a Taylor series up to the first or second order term. Then by subtrac

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