In this paper some common used numerical schemes for solving discrete ordinate equations are considered and the error estimates are studied for the combined spatial and angular approximations. The conclusions show tha...
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In this paper some common used numerical schemes for solving discrete ordinate equations are considered and the error estimates are studied for the combined spatial and angular approximations. The conclusions show that the error order of scalar flux in all of these schemes can not be second order even if the source term f is smooth enough. In addition, when we introduce a kind of graded grids, the simple step character scheme has same accuracy as "high order" ones.
In this paper, the convergence of discrete flux in the difference scheme for the linear parabolic equation with discontinuous coefficients is disucssed. It is shown that the discrete flux of the difference scheme tend...
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In this paper, the convergence of discrete flux in the difference scheme for the linear parabolic equation with discontinuous coefficients is disucssed. It is shown that the discrete flux of the difference scheme tends to the continuous flux of the differential equation in the sense of the maximum norm and the rate of convergence is O( r+ h1/2).
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.
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