基于加密物理片的数值流形法中局部网格加密

发布时间：2018-03-10 04:26

  本文选题：数值流形法　切入点：加密物理片　出处：《岩土力学》2017年04期 　论文类型：期刊论文

【摘要】：数值流形法的数学网格不需要适应求解域内各种不连续界面和边界,因此,总可以用规则的结构化网格建立数学覆盖。但对于大多数问题,在整个求解域上布置统一密度的网格显得浪费。因此,需要研究在结构化网格上实施局部加密,建立了加密物理片的方法用以解决这一问题。具体的实施过程中,确定了需要加密的区域后,先在这些区域布置规则的精细网格,然后找到这些区域中包含的原始网格中的物理片,用精细网格上建立的插值代替被加密物理片上的局部近似,从而提高了局部近似的阶次。数值算例结果表明,该方法收敛性良好。另外,如果所有物理片上的局部近似都采用0阶多项式(常数),那么将会得到正定的刚度矩阵。
[Abstract]:The mathematical mesh of the numerical manifold method does not need to be adapted to solve various discontinuous interfaces and boundaries in the domain, so it is always possible to establish a mathematical cover with regular structured meshes. But for most problems, It is wasteful to arrange uniform density grids in the whole solution domain. Therefore, it is necessary to study the implementation of local encryption on structured grids, and to establish a method of encrypting physical slices to solve this problem. After the regions that need encryption are determined, regular fine grids are arranged in these areas first, then the physical slices in the original grids contained in these areas are found, and the interpolation established on the fine grids is used to replace the local approximation on the encrypted physical slices. As a result, the order of local approximation is improved. The numerical results show that the method converges well. In addition, if all the local approximations on the physical chip adopt the polynomial of order 0 (constant), then the positive definite stiffness matrix will be obtained.
【作者单位】： 中国科学院武汉岩土力学研究所岩土力学与工程国家重点实验室;湖北省水利水电科学研究院;
【基金】：国家自然科学基金项目(No.11572009,No.51538001)~~
【分类号】：O241.3
，

本文编号：1591762