Numerical Methods for Advancing Interfaces
نویسنده
چکیده
A propagating interface can develop corners and discontinuities as it advances. The level set algorithm such as the fast marching method (FMM) has been extensively applied in simulating advancing fronts. However, it is a rstorder scheme and hard to incorporate higher-order schemes in realistic media; it costs O(N log2N), where N is the number of grid points. The article is concerned with the development of two algorithms of cost O(N): the group marching method (GMM) and ENO-DNO-PS. GMM is a variant of FMM and advances a selected group of grid points at a time, rather than sorting the solution in the narrow band to march forward a single grid point. ENO-DNO-PS is a second-order ENO scheme for which stability is enforced by the introduction of a down 'n' out (DNO) marching scheme and a post sweeping (PS) iteration. Various techniques are introduced to improve the numerical accuracy and stability. The algorithms are implemented for the eikonal equation in three dimensions (3D) to demonstrate and compare their accuracy and e ciency.
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Computational Methods for Advancing Interfaces
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