计算三维体积的四边形等参元方法  

COMPUTING 3-D VOLUME WITH QUADRANGLE ISOPARAMETRIC ELEMENT METHOD

作　　者：钟尔杰[1] 罗志强[1] 

机构地区：[1]电子科技大学应用数学学院,成都610054

出　　处：《数值计算与计算机应用》2006年第2期106-113,共8页Journal on Numerical Methods and Computer Applications

摘　　要：通过对三维有界区域的边界曲面作四边形网格剖分,用有限元方法处理高斯公式中的曲面积分,由等参变换及双线性插值导出任意四边形单元上曲面积分的数值求积公式．分析求积公式中三阶行列式意义,提出了简单五面体有向体积概念,推导出计算四边形网面所围立体的有向体积叠加方法．数值试验表明该方法对光滑边界三维体积计算有很好的数值逼近．Boundary surface of 3-D region is divided into quadrangle mesh, the surface integral in Gauss formula is treated with finite element method. The quadrature formula about surface integral on any quadrilateral element is deduced by means of isoparametric transformation and bilinear interpolation. This paper analyzes the meaning of 3-order determinant and the concept of directed volume of simple pentahedron is presented. The formula of summing directed volume, about volume of solid that is surrounded by quadrangle mesh is derived in here. The numerical test show this method have good numerical approximation for 3-D volume which has smooth boundary surface.

关 键 词：高斯公式 四边形网面 等参变换 有向体积 

分 类 号：O241.82[理学—计算数学]