基于独立覆盖的流形法的收敛性及覆盖网格特性

针对前期提出的基于部分重叠覆盖的数值流形方法,将其内涵范围缩小,仅研究其中的一种情况——基于独立覆盖的数值流形方法。从完备性和协调性2个方面讨论该方法的收敛性,特别强调其收敛性是基于各个独立覆盖的逼近而建立起来的,独立覆盖之间条形连接区域的尺寸要取小,并由此推断及用实例说明,覆盖网格可以具备“3个任意”的优良特性——任意形状、任意连接以及由此而来的可任意加密的能力,从而有望使数值计算的前处理工作大为简化。

Characteristics of Convergence and Cover Mesh in Numerical Manifold Method Based on Independent Covers

The scope of a numerical manifold method (NMM) based on partially overlapping covers is narrowed to a special case based on independent covers. Convergence of the new method is discussed from two aspects: completeness and coordination. The convergence of the method is due to the convergence of each independent cover. Results show that the size of the strips between independent covers should be small. Moreover, the cover meshes have three excellent features: arbitrary shape, arbitrary connection, and arbitrary refinement. Finally, some illustrations are given to verify these “arbitrary” features, and the method can be used to greatly simplify the pre-processing of numerical analysis.