Numerical Solution of the Generalized Airfoil Equation for an Airfoil with a Flap
SIAM Journal on Numerical Analysis
A Collocation Method for the Generalized Airfoil Equation for an Airfoil with a Flap
SIAM Journal on Numerical Analysis
High order methods for weakly singular integral equations with nonsmooth input functions
Mathematics of Computation
A generalisation of Telles' method for evaluating weakly singular boundary element integrals
Journal of Computational and Applied Mathematics
Transformations for evaluating singular boundary element integrals
Journal of Computational and Applied Mathematics
Transformations for evaluating singular boundary element integrals
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
Improved singular boundary method for elasticity problems
Computers and Structures
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Accurate numerical integration of line integrals is of fundamental importance for the reliable implementation of the boundary element method. Usually, the regular integrals arising from a boundary element method implementation are evaluated using standard Gaussian quadrature. However, the singular integrals which arise are often evaluated in another way, sometimes using a different integration method with different nodes and weights.This paper presents a straightforward transformation to improve the accuracy of evaluating singular integrals. The transformation is, in a sense, a generalisation of the popular method of Telles with the underlying idea being to utilise the same Gaussian quadrature points as used for evaluating nonsingular integrals in a typical boundary element method implementation. The new transformation is also shown to be equivalent to other existing transformations in certain situations.Comparison of the new method with existing coordinate transformation techniques shows that a more accurate evaluation of weakly singular integrals can be obtained. The technique can also be extended to evaluate certain Hadamard finite-part integrals. Based on the observation of several integrals considered, guidelines are suggested for the best transformation order to use (i.e. the degree to which nodes should be clustered near the singular point).