GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Removing the stiffness from interfacial flows with surface tension
Journal of Computational Physics
Journal of Computational Physics
Microstructural evolution in inhomogeneous elastic media
Journal of Computational Physics
Numerical Calculation of Three-Dimensional Interfacial Potential Flows Using the Point Vortex Method
SIAM Journal on Scientific Computing
Axisymmetric Vortex Sheet Motion: Accurate Evaluation of the Principal Value Integral
SIAM Journal on Scientific Computing
Boundary integral methods for multicomponent fluids and multiphase materials
Journal of Computational Physics
The nonlinear evolution of vortex sheets with surface tension in axisymmetric flows
Journal of Computational Physics
Efficient semi-implicit schemes for stiff systems
Journal of Computational Physics
A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains
Journal of Computational Physics
Hi-index | 31.45 |
Many applications in materials involve surface diffusion of elastically stressed solids. Study of singularity formation and long-time behavior of such solid surfaces requires accurate simulations in both space and time. Here we present a high-order boundary integral method for an elastically stressed solid with axi-symmetry due to surface diffusions. In this method, the boundary integrals for isotropic elasticity in axi-symmetric geometry are approximated through modified alternating quadratures along with an extrapolation technique, leading to an arbitrarily high-order quadrature; in addition, a high-order (temporal) integration factor method, based on explicit representation of the mean curvature, is used to reduce the stability constraint on time-step. To apply this method to a periodic (in axial direction) and axi-symmetric elastically stressed cylinder, we also present a fast and accurate summation method for the periodic Green's functions of isotropic elasticity. Using the high-order boundary integral method, we demonstrate that in absence of elasticity the cylinder surface pinches in finite time at the axis of the symmetry and the universal cone angle of the pinching is found to be consistent with the previous studies based on a self-similar assumption. In the presence of elastic stress, we show that a finite time, geometrical singularity occurs well before the cylindrical solid collapses onto the axis of symmetry, and the angle of the corner singularity on the cylinder surface is also estimated.