数值计算与计算机应用
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数值计算与计算机应用  2011, Vol. 32 Issue (1): 33-40    DOI:
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含曲率的水平集方程在非结构四边形网格上的数值离散方法
程俊霞, 任健
北京应用物理与计算数学研究所, 北京 100094
NUMERICAL SCHEMES FOR THE LEVEL SET EQUATIONS ON UNSTRUCTURED QUADRILATERAL MESHES
Cheng Junxia, Ren Jian
Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
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摘要 

在非结构四边形网格上, 含曲率的水平集方程采用伽辽金等参有限元方法空间离散,时间离散采用半隐格式. 离散形成的线性方程组的系数矩阵是对称的稀疏矩阵, 采用共轭梯度法求解. 数值算例表明,在笛卡儿网格和随机网格上,含曲率的水平集方程离散格式可达到近似二阶精度. 重新初始化方程的离散格式精度可达到近似一阶精度.给出了非结构四边形网格上不光滑界面以曲率收缩的运动过程.在不采用重新初始化的情况下, 收缩过程未出现不稳定现象.

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关键词水平集方程   非结构四边形网格   伽辽金等参有限元方法     
Abstract

Level set equations containing curvature are solved on unstructured quadrilateral meshes. We use spatial discretization by the Galerkin isoparametric finite element method, and semi-implicit time stepping. Conjugate gradient method solves the linear system of equations, whose coefficient matrix is symmetric and sparse. On Cartesian meshes and random meshes, the scheme of level set equations containing curvature is nearly second order accuracy in L2 and L norms. Example is given of nonsmooth level sets shortening stably without reinitialization by local curvature on unstructured quadrilateral meshes.

Key wordslevel set equations   unstructured quadrilateral meshes   Galerkin isoparametric finite element method   
收稿日期: 2010-03-11;
基金资助:

中物院院基金(20050107), 中物院科技发展基金(2007A09006), 实验室基金(9140C690101070C69), 国家重大基础研究基金(2005CB32170), 实验室基金(9140C6901030803), 国家自然科学基金(10901022)资助项目.

引用本文:   
. 含曲率的水平集方程在非结构四边形网格上的数值离散方法[J]. 数值计算与计算机应用, 2011, 32(1): 33-40.
. NUMERICAL SCHEMES FOR THE LEVEL SET EQUATIONS ON UNSTRUCTURED QUADRILATERAL MESHES[J]. Journal of Numerical Methods and Computer Applicat, 2011, 32(1): 33-40.
 
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