• 대한기계학회논문집B
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• 제29권6호
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• pp.703-710
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• 2005

A finite element discretization of the advection and redistancing equations of level set method has been studied. It has been shown that Galerkin spatial discretization combined with Crank-Nicolson temporal discretization of the advection equation of level set yields a good result and that consistent streamline upwind Petrov-Galerkin(CSUPG) discretization of the redistancing equation gives satisfactory solutions for two test problems while the solutions of streamline upwind Petrov-Galerkin(SUPG) discretization are dissipated by the numerical diffusion added for the stability of a hyperbolic system. Furthermore, it has been found that the solutions obtained by CSUPG method are comparable to those by second order ENO method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제16권1호
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• pp.31-49
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• 2012

In this paper, we propose a very efficient method which reconstructs the high resolution surface from a set of unorganized points. Our method is based on the level set method using adaptive octree. We start with the surface reconstruction model proposed in [20]. In [20], they introduced a very fast and efficient method which is different from the previous methods using the level set method. Most existing methods[21, 22] employed the time evolving process from an initial surface to point cloud. But in [20], they considered the surface reconstruction process as an elliptic problem in the narrow band including point cloud. So they could obtain very speedy method because they didn't have to limit the time evolution step by the finite speed of propagation. However, they implemented that model just on the uniform grid. So they still have the weakness that it needs so much memories because of being fulfilled only on the uniform grid. Their algorithm basically solves a large linear system of which size is the same as the number of the grid in a narrow band. Besides, it is not easy to make the width of band narrow enough since the decision of band width depends on the distribution of point data. After all, as far as it is implemented on the uniform grid, it is almost impossible to generate the surface on the high resolution because the memory requirement increases geometrically. We resolve it by adapting octree data structure[12, 11] to our problem and by introducing a new redistancing algorithm which is different from the existing one[19].