In this paper, a new method of topological cleanup for quadrilateral mesh is presented. The method first selects a patch of mesh around an irregular node. It then seeks the best connection of the selected patch accord...In this paper, a new method of topological cleanup for quadrilateral mesh is presented. The method first selects a patch of mesh around an irregular node. It then seeks the best connection of the selected patch according to its irregular valence using a new topological operation： small polygon reconnection （SPR）. By replacing the original patch with an optimal one that has less irregular valence, mesh quality can be improved. Three applications based on the proposed approach are enumerated： （1） improving the quality of a quadrilateral mesh, （2） converting a triangular mesh to a quadrilateral one, and （3） adapting a triangle generator to a quadrilateral one. The presented method is highly effective in all three applications.展开更多
In order to study the constitutive behavior of concrete in mesoscopic level, a new method is proposed in this paper. This method uses random polygon particles to simulate full grading broken aggregates of concrete. Ba...In order to study the constitutive behavior of concrete in mesoscopic level, a new method is proposed in this paper. This method uses random polygon particles to simulate full grading broken aggregates of concrete. Based on computational geometry, we carry out the automatic generation of the triangle finite element mesh for the model of random polygon particles of concrete. The finite element mesh generated in this paper is also applicable to many other numerical methods.展开更多
应变-旋转(Strain-Rotation,S-R)和分解定理为分析几何非线性问题提供了合理可靠的理论基础,但用有限元求解时会遇到大变形发生后的网格畸变问题。近年提出的虚单元法(Virtual element method,VEM)适用于一般的多边形网格,因此,该文尝...应变-旋转(Strain-Rotation,S-R)和分解定理为分析几何非线性问题提供了合理可靠的理论基础,但用有限元求解时会遇到大变形发生后的网格畸变问题。近年提出的虚单元法(Virtual element method,VEM)适用于一般的多边形网格,因此,该文尝试使用一阶虚单元求解基于S-R和分解定理的二维几何非线性问题,以克服网格畸变的影响。基于重新定义的多项式位移空间基函数,推演获得一阶虚单元分析线弹性力学问题时允许位移空间向多项式位移空间的投影表达式;按照虚单元法双线性格式的计算规则,分析处理基于更新拖带坐标法和势能率原理的增量变分方程;进而建立离散系统方程及其矩阵表达形式,并编制MATLAB求解程序;采用常规多边形网格和畸变网格,应用该文算法分析均布荷载下的悬臂梁和均匀内压下的厚壁圆筒变形。结果与已有文献和ANSYS软件的对比表明:该文算法在两种网格中均可有效执行且具备足够数值精度。总体该文算法为基于S-R和分解定理的二维几何非线性问题求解提供了一种鲁棒方法。展开更多
Two-dimensional mesh-based motion tracking preserves neighboring relations (through connectivity of the mesh) and also allows warping transformations between pairs of frames;thus, it effectively eliminates blocking ar...Two-dimensional mesh-based motion tracking preserves neighboring relations (through connectivity of the mesh) and also allows warping transformations between pairs of frames;thus, it effectively eliminates blocking artifacts that are common in motion compensation by block matching. However, available uniform 2-D mesh model enforces connec-tivity everywhere within a frame, which is clearly not suitable across occlusion boundaries. To overcome this limitation, BTBC (background to be covered) detection and MF (model failure) detection algorithms are being used. In this algorithm, connectivity of the mesh elements (patches) across covered and uncovered region boundaries are broken. This is achieved by allowing no node points within the background to be covered and refining the mesh structure within the model failure region at each frame. We modify the occlusion-adaptive, content-based mesh design and forward tracking algorithm used by Yucel Altunbasak for selection of points for triangular 2-D mesh design. Then, we propose a new triangulation procedure for mesh structure and also a new algorithm to justify connectivity of mesh structure after motion vector estimation of the mesh points. The modified content-based mesh is adaptive which eliminates the necessity of transmission of all node locations at each frame.展开更多
Based on the idea of serendipity element,we construct and analyze the first quadratic serendipity finite volume element method for arbitrary convex polygonalmeshes in this article.The explicit construction of quadrati...Based on the idea of serendipity element,we construct and analyze the first quadratic serendipity finite volume element method for arbitrary convex polygonalmeshes in this article.The explicit construction of quadratic serendipity element shape function is introduced from the linear generalized barycentric coordinates,and the quadratic serendipity element function space based on Wachspress coordinate is selected as the trial function space.Moreover,we construct a family of unified dual partitions for arbitrary convex polygonal meshes,which is crucial to finite volume element scheme,and propose a quadratic serendipity polygonal finite volume element method with fewer degrees of freedom.Finally,under certain geometric assumption conditions,the optimal H1 error estimate for the quadratic serendipity polygonal finite volume element scheme is obtained,and verified by numerical experiments.展开更多
基金supported by the National Natural Science Foundation of China (10972006, 11172004)National Basic Research Program of China (2010CB832701)
文摘In this paper, a new method of topological cleanup for quadrilateral mesh is presented. The method first selects a patch of mesh around an irregular node. It then seeks the best connection of the selected patch according to its irregular valence using a new topological operation： small polygon reconnection （SPR）. By replacing the original patch with an optimal one that has less irregular valence, mesh quality can be improved. Three applications based on the proposed approach are enumerated： （1） improving the quality of a quadrilateral mesh, （2） converting a triangular mesh to a quadrilateral one, and （3） adapting a triangle generator to a quadrilateral one. The presented method is highly effective in all three applications.
文摘In order to study the constitutive behavior of concrete in mesoscopic level, a new method is proposed in this paper. This method uses random polygon particles to simulate full grading broken aggregates of concrete. Based on computational geometry, we carry out the automatic generation of the triangle finite element mesh for the model of random polygon particles of concrete. The finite element mesh generated in this paper is also applicable to many other numerical methods.
文摘应变-旋转(Strain-Rotation,S-R)和分解定理为分析几何非线性问题提供了合理可靠的理论基础,但用有限元求解时会遇到大变形发生后的网格畸变问题。近年提出的虚单元法(Virtual element method,VEM)适用于一般的多边形网格,因此,该文尝试使用一阶虚单元求解基于S-R和分解定理的二维几何非线性问题,以克服网格畸变的影响。基于重新定义的多项式位移空间基函数,推演获得一阶虚单元分析线弹性力学问题时允许位移空间向多项式位移空间的投影表达式;按照虚单元法双线性格式的计算规则,分析处理基于更新拖带坐标法和势能率原理的增量变分方程;进而建立离散系统方程及其矩阵表达形式,并编制MATLAB求解程序;采用常规多边形网格和畸变网格,应用该文算法分析均布荷载下的悬臂梁和均匀内压下的厚壁圆筒变形。结果与已有文献和ANSYS软件的对比表明:该文算法在两种网格中均可有效执行且具备足够数值精度。总体该文算法为基于S-R和分解定理的二维几何非线性问题求解提供了一种鲁棒方法。
文摘Two-dimensional mesh-based motion tracking preserves neighboring relations (through connectivity of the mesh) and also allows warping transformations between pairs of frames;thus, it effectively eliminates blocking artifacts that are common in motion compensation by block matching. However, available uniform 2-D mesh model enforces connec-tivity everywhere within a frame, which is clearly not suitable across occlusion boundaries. To overcome this limitation, BTBC (background to be covered) detection and MF (model failure) detection algorithms are being used. In this algorithm, connectivity of the mesh elements (patches) across covered and uncovered region boundaries are broken. This is achieved by allowing no node points within the background to be covered and refining the mesh structure within the model failure region at each frame. We modify the occlusion-adaptive, content-based mesh design and forward tracking algorithm used by Yucel Altunbasak for selection of points for triangular 2-D mesh design. Then, we propose a new triangulation procedure for mesh structure and also a new algorithm to justify connectivity of mesh structure after motion vector estimation of the mesh points. The modified content-based mesh is adaptive which eliminates the necessity of transmission of all node locations at each frame.
基金supported by the National Natural Science Foundation of China(Nos.11871009,12271055)the Foundation of LCP and the Foundation of CAEP(CX20210044).
文摘Based on the idea of serendipity element,we construct and analyze the first quadratic serendipity finite volume element method for arbitrary convex polygonalmeshes in this article.The explicit construction of quadratic serendipity element shape function is introduced from the linear generalized barycentric coordinates,and the quadratic serendipity element function space based on Wachspress coordinate is selected as the trial function space.Moreover,we construct a family of unified dual partitions for arbitrary convex polygonal meshes,which is crucial to finite volume element scheme,and propose a quadratic serendipity polygonal finite volume element method with fewer degrees of freedom.Finally,under certain geometric assumption conditions,the optimal H1 error estimate for the quadratic serendipity polygonal finite volume element scheme is obtained,and verified by numerical experiments.
