A number of numerical simulations of surfaces evolving by mean curvature in anisotropic materials are presented and discussed. We approximate an evolution law based on an appropriate definition of anisotropic mean curvature. This is first regularized by means of a relaxation procedure that produces a reaction-diffusion equation similar to the model proposed by Allen and Cahn for the evolution of antiphase boundaries. The successive discretization process is based on linear finite elements in space and forward differences in time. The final algorithm also exploits the localized behaviour of the solution using a dynamically maintained mesh that spans the sole transition region of the relaxed solution, corresponding to a thin strip around the moving interface.
Paolini, M., An efficient algorithm for computing anisotropic evolution by mean curvature, Contributed paper, in Curvature flows and related topics, (Levico Terme, 28-June 02-July 1994), Gakkotosho, Tokyo 1995: 199-213 [http://hdl.handle.net/10807/23494]
An efficient algorithm for computing anisotropic evolution by mean curvature
Paolini, Maurizio
1995
Abstract
A number of numerical simulations of surfaces evolving by mean curvature in anisotropic materials are presented and discussed. We approximate an evolution law based on an appropriate definition of anisotropic mean curvature. This is first regularized by means of a relaxation procedure that produces a reaction-diffusion equation similar to the model proposed by Allen and Cahn for the evolution of antiphase boundaries. The successive discretization process is based on linear finite elements in space and forward differences in time. The final algorithm also exploits the localized behaviour of the solution using a dynamically maintained mesh that spans the sole transition region of the relaxed solution, corresponding to a thin strip around the moving interface.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.