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Second-order accurate computation of curvatures in a level set framework using novel high-order reinitialization schemes. (English) Zbl 1203.65043
Summary: We present a high-order accurate scheme for the reinitialization equation of {\it M. Sussman, P. Smereka} and {\it S. Osher} [J. Comput. Phys. 114, No. 1, 146--159 (1994; Zbl 0808.76077)] that guarantees accurate computation of the interface’s curvatures in the context of level set methods. This scheme is an extension of the work of {\it G. Russo} and {\it P. Smereka} [J. Comput. Phys. 163, No. 1, 51--67 (2000; Zbl 0964.65089)]. We present numerical results in two and three spatial dimensions to demonstrate fourth-order accuracy for the reinitialized level set function, third-order accuracy for the normals and second-order accuracy for the interface’s mean curvature in the $L ^{1}$- and $L ^{\infty }$-norms. We also exploit the work of {\it Ch. Min} and {\it F. Gibou} [J. Comput. Phys. 225, No. 1, 300--321 (2007; Zbl 1122.65077)] to show second-order accurate scheme for the computation of the mean curvature on non-graded adaptive grids.

MSC:
65D18Computer graphics, image analysis, and computational geometry
53C44Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
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References:
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