An efficient boundary integral method for the Mullins-Sekerka problem

We use a boundary integral technique to study the two space dimensional Mullins-Sekerka free boundary problem which originates from a study of solidification and liquidation of materials of negligible specific heat. This is an area preserving and curve shortening motion. Evolution equations for the free boundaries are derived in terms of the tangent angle and total arclength, which makes a small scale decomposition possible and the Fourier transform a powerful tool in numerical calculations. With this formulation, implicit schemes can be implemented to avoid the difficult numerical stiffness associated with explicit schemes. We can compute solutions up to the time when there is a topological change, i.e., when particles touch or break up. Our numerical results for systems of a single particle or multi-particles provide some valuable information in the particle dynamics, such as the circularization of each individual particle, and the mass transfer between different particles during particle interactions. (C) 1996 Academic Press, Inc.