数值流形法独立覆盖区域的一种自动选取方法

An Algorithm for Automatic Selection of Independent Cover Regions of Numerical Manifold Method

部分重叠覆盖的数值流形法是一种以独立覆盖为主的分析方式。为了在常规尺寸单元的数学网格中自动选取独立覆盖区域,应用图的着色方法将数学网格的单元分为若干个独立集。在此基础上,以独立覆盖区域最多为原则,选择用于定义独立覆盖的单元(其所有结点覆盖合并为一个覆盖),其余单元作为重叠区域以保持连续性,不属于独立覆盖单元的结点作为常规的结点覆盖。通过算例,揭示了重叠覆盖间的线性相关仅存在于数学网格边界上的结点覆盖,覆盖合并可以减少整体刚度矩阵零特征值的数目,甚至完全避免线性相关。

Numerical manifold method with partially overlapping covers is an analysis mode mainly concerning inde- pendent covers. To automatically select independent cover regions in a mathematical mesh with general element size, the elements of the mathematical mesh are partitioned into a number of independent sets by graph colouring. Based on this, the elements for defining independent covers （ i. e. the covers of all nodes of an element are merged into single one） are selected according to the principle of as many regions with independent covers as possible, and the rest of elements is defined as the overlapping cover regions for keeping the continuity, and the nodes which do not belong to the independent cover elements are defined as general nodal covers. Examples reveal that the linear dependencies between the overlapping covers exist only in the nodal covers on the mathematical mesh boundary, and cover merging could reduce the nullity of stiffness matrix or even avoid the linear dependencies.