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In the course of tuning the developed numerical algorithm for MR-DTI data visualization, it was necessary to introduce a measurement technique capable of quantitatively assessing the artificial isotro...pic diffusion in numerical schemes for PDE. Based on such assessment, a qualified choice of the numerical scheme can be made. This contribution describes the proposed measurement technique based on total variation evaluation. The procedure is applied to several numerical discretizations of the anisotropic diffusion model based on the Allen-Cahn equation and the obtained results are presented. For comparison, the traditional experimental order of convergence measurements are also provided to show their irrelevance in numerical diffusion quantification for the studied problem.続きを見る
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1.Introduction 2.Problem for the Allen-Cahn Equation with Anisotropy 3.Artificial Diffusion Measurement
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