|| We review a variable transformation method proposed by the author and co-workers for evaluating nearly singular integrals over curved surfaces appearing in the boundary element method.
The method introduces polar coordinates centred at the source projection, and then employs radial and angular variable transformations to weaken the near singularity before applying standard quadrature. Several radial variable transformations, which are particularly important in the method, will be presented. Then, error analysis using complex function theory yields insight regarding the optimal radial variable transformation.
Finally, we will discuss the efficient use of the double exponential transformation in the radial variable transformation.