Numerical Simulations of Unsteady Crystal Growth

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Abstract
An efficient algorithm is developed to numerically compute solutions of problems related to crystal growth. The method is based on an integral equation formulation that involves an integration over the entire history of the growth. A direct calculation of this memory integral becomes more costly as time increases, but an indirect method is presented that has a fixed operation cost per timestep. The one-dimensional procedure is tested and applied to the problem of rapid directional solidification where the nonlinear development of a recently discovered oscillatory instability is followed.