A Numerical Scheme for the Two Phase Mullins-Sekerka Problem

Bates, Peter W.
Chen, Xinfu
Deng, Xinyu
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Southwest Texas State University, Department of Mathematics
An algorithm is presented to numerically treat a free boundary problem arising in the theory of phase transition. The problem is one in which a collection of simple closed curves (particles) evolves in such a way that the enclosed area remains constant while the total arclength decreases. Material is transported between particles and within particles by diffusion, driven by curvature which expresses the effect of surface tension. The algorithm is based on a reformulation of the problem, using boundary integrals, which is then discretized and cast as a semi-implicit scheme. This scheme is implemented with a variety of configurations of initial curves showing that convexity or even topological type may not be preserved.
Boundary integral, Free boundary problem, Motion by curvature, Ostwald ripening
Bates, P. W., Chen, X., Deng, X. (1995). A numerical scheme for the two phase Mullins-Sekerka problem. <i>Electronic Journal of Differential Equations, 1995</i>(11), pp. 1-28.