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有理Bézier单元求解参数曲面上Laplace-Beltrami方程
外文标题:Solving Laplace-Beltrami Equation on Parametric Surface by Rational Bézier Elements
文献类型:期刊
作者:Chen, Tao[1]  Mo, Rong[2]  Wan, Neng[3]  Xiang, Ying[4]  
机构:[1]Key Laboratory of Contemporary Design and Integrated Manufacturing Technology, Ministry of Education, Northwestern Polytechnical University, Xi'an 710072, China
[2]Key Laboratory of Contemporary Design and Integrated Manufacturing Technology, Ministry of Education, Northwestern Polytechnical University, Xi'an 710072, China
[3]Key Laboratory of Contemporary Design and Integrated Manufacturing Technology, Ministry of Education, Northwestern Polytechnical University, Xi'an 710072, China
[4]Key Laboratory of Contemporary Design and Integrated Manufacturing Technology, Ministry of Education, Northwestern Polytechnical University, Xi'an 710072, China
通讯作者:Chen, T.(chentaonwpu@163.com)
年:2014
期刊名称:计算机辅助设计与图形学学报
卷:26
期:3
页码范围:385-391
增刊:正刊
收录情况:EI(20141417541437)  
人气指数:3120
浏览次数:3090
基金:国家自然科学基金; 陕西省自然科学基础研究计划; 西北工业大学基础研究基金
关键词:有理Bézier单元 Galerkin法 偏微分方程 流形曲面 Laplace-Beltrami方程 rational Bézier element Galerkin method partial differential equation manifold surface Laplace-Beltrami equation
摘要:用有限元法数值求解时,定义在流形曲面上的偏微分方程的数值解精度会因为传统多边形单元的几何逼近误差而严重降低,为此提出基于有理Bernstein多项式的几何精确有限元法.首先插入重复节点从NURBS曲面直接生成有理Bézier单元,这一过程保持原有几何不变;然后通过Galerkin法建立参数曲面上包含Laplace-Beltrami微分算子的二阶椭圆偏微分方程的等效弱形式;针对Bernstein基函数的非插值性,通过配点法施加Dirichlet类型的边界约束,得到最优收敛的离散格式.数值算例结果表明,该方法能有效地减少网格离散误差,提高分析结果精度.
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