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Keywords:
interface evolution; anisotropic energy; weighted mean curvature; obstacle problem; thresholding method; convolution kernels; topology change; numerical analysis
interface evolution; anisotropic energy; weighted mean curvature; obstacle problem; thresholding method; convolution kernels; topology change; numerical analysis
Summary:
We extend thresholding methods for numerical realization of mean curvature flow on obstacles to the anisotropic setting where interfacial energy depends on the orientation of the interface. This type of schemes treats the interface implicitly, which supports natural implementation of topology changes, such as merging and splitting, and makes the approach attractive for applications in material science. The main tool in the new scheme are convolution kernels developed in previous studies that approximate the given anisotropy in a nonlocal way. We provide a detailed report on the numerical properties of the proposed algorithm.
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