A high-order boundary integral method was presented for treating an elastically stressed solid having axi-symmetry due to surface diffusion. In this method, the boundary integrals for isotropic elasticity in an axi-symmetrical geometry were approximated by modified alternating quadratures; together with an extrapolation technique. This led to an arbitrarily high-order quadrature. In addition, a high-order (temporal) integration factor method, based upon explicit representation of the mean curvature, was used to reduce the stability constraint on time-steps. In order to apply this method to a periodic (axial direction) and axi-symmetrical elastically stressed cylinder, a fast and accurate summation method for the periodic Green’s functions of isotropic elasticity was also presented. Using the high-order boundary integral method it was demonstrated, that in the absence of elasticity, the cylinder surface pinched in finite time at the axis of the symmetry and the universal cone-angle of the pinching was found to be consistent with previous results which had been based upon a self-similar assumption. In the presence of elastic stresses, it was shown that a finite-time geometrical singularity occurred well before the

cylindrical solid collapsed onto the axis of symmetry. The angle of the corner singularity on the cylinder surface was also estimated.

A High-Order Boundary Integral Method for Surface Diffusions on Elastically Stressed Axisymmetric Rods. X.Li, Q.Nie: Journal of Computational Physics, 2009, 228[12], 4625-37