Automatic Differentiation For The Evaluation Of Singular Integrals In Two-dimensional Boundary Element Computations
Price
Free (open access)
Transaction
Volume
19
Pages
10
Published
1997
Size
713 kb
Paper DOI
10.2495/BE970661
Copyright
WIT Press
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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