Delaunay triangulation has been widely used in many fields such as compu- tational fluid dynamics, statistics, meteorology solid state physics, computational geometry and so on. Bowyer-Watson algorithm is a very popul...
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Delaunay triangulation has been widely used in many fields such as compu- tational fluid dynamics, statistics, meteorology solid state physics, computational geometry and so on. Bowyer-Watson algorithm is a very popular one for generating Delaunay triangulation. In generating the Delaunay triangulation of a preassigned set of n points, the complexity of Bowyer-Watson algorithm can at most be reduced to O(n log n) for the simple reason that the complexity of its tree search process is O(nlog n). In this paper we suggest a tree search technique whose complexity is O(n). Noting that the order of point insertion can affect the efficiency of Bowyer- Watson algorithm, we propose a technique to optimize the point insertion process. Based on these two techniques, we obtain a fast algorithm for generating Delaunay triangulation.
In this paper, a numerical method is developed for solving one-dimensional hyperbolic system of conservation laws by the Taylor-Galerkin finite element method. The scheme is obtained by solving conservation equations ...
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In this paper, a numerical method is developed for solving one-dimensional hyperbolic system of conservation laws by the Taylor-Galerkin finite element method. The scheme is obtained by solving conservation equations associated HamiltonJacobi equations. The scheme has the TVD-like property under the uniform meshes. Numerical examples are given.
Some nonlinear coupled problems of hyperbolic and parabolic equations are considered, the finite element scheme and A. D. I. finite element scheme are studied. The existence and uniqueness of the approximational schem...
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Some nonlinear coupled problems of hyperbolic and parabolic equations are considered, the finite element scheme and A. D. I. finite element scheme are studied. The existence and uniqueness of the approximational schemes are obtained, together with the optimal H 1-norm and L 2-norm convergence results.
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