Abstract
This paper presents a study of the performance of the nonโlinear coโordinate transformations in the numerical integration of weakly singular boundary integrals. A comparison of the smoothing property, numerical convergence and accuracy of the available nonโlinear polynomial transformations is presented for twoโdimensional problems. Effectiveness of generalized transformations valid for any type and location of singularity has been investigated. It is found that weakly singular integrals are more efficiently handled with transformations valid for endโpoint singularities by partitioning the element at the singular point. Further, transformations which are excellent for CPV integrals are not as accurate for weakly singular integrals. Connection between the maximum permissible order of polynomial transformations and precision of computations has also been investigated; cubic transformation is seen to be the optimum choice for single precision, and quartic or quintic one, for double precision computations. A new approach which combines the method of singularity subtraction with nonโlinear transformation has been proposed. This composite approach is found to be more accurate, efficient and robust than the singularity subtraction method and the nonโlinear transformation methods. Copyright ยฉ 2001 John Wiley & Sons, Ltd.