期刊
COMMUNICATIONS IN APPLIED MATHEMATICS AND COMPUTATIONAL SCIENCE
卷 9, 期 1, 页码 107-141出版社
MATHEMATICAL SCIENCE PUBL
DOI: 10.2140/camcos.2014.9.107
关键词
implicit surfaces; closest point; level set methods; reinitialisation; redistancing; high-order
资金
- Luis W. Alvarez Postdoctoral Fellowship at Lawrence Berkeley National Laboratory
- Laboratory Directed Research and Development Program of LBNL
- U.S. DOE Office of Advanced Scientific Computing Research [DE-AC02-05CH11231]
Implicitly embedding a surface as a level set of a scalar function phi : R-d -> R is a powerful technique for computing and manipulating surface geometry. A variety of applications, e.g., level set methods for tracking evolving interfaces, require accurate approximations of minimum distances to or closest points on implicitly defined surfaces. In this paper, we present an efficient method for calculating high-order approximations of closest points on implicit surfaces, applicable to both structured and unstructured meshes in any number of spatial dimensions. In combination with a high-order approximation of phi, the algorithm uses a rapidly converging Newton's method initialised with a guess of the closest point determined by an automatically generated point cloud approximating the surface. In general, the order of accuracy of the algorithm increases with the approximation order of phi. We demonstrate orders of accuracy up to six for smooth problems, while nonsmooth problems reliably reduce to their expected order of accuracy. Accompanying this paper is C++ code that can be used to implement the algorithms in a variety of settings.
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