单位分解

有限覆盖和单位分解是单位分解积分的数学基础，对单位分解积分进行了严格证明，并指出使用Shepard函数作为单位分解函数是一个很好的选择。

Partition of unity quadrature is shown strictly with finite covering and partition of unity . Using Shepard functions as partition of unity functions , we obtain good results .

关于多复变数的全纯支撑函数和单位分解

On holomorphic support function and partition of unity in several complex variables

无需网格地构成了Shepard单位分解函数。

The Shepard function of PU was constructed without meshing .

该方法基于单位分解（PU）框架，定义了带分析信息的增强覆盖函数，建立场量函数的近似公式表达。

Under the framework of partition of unit ( PU ) in the method , enrichment cover functions with the known analyzed information were defined , and the formulation of approximate field function was built .

单位分解增强自然单元法计算应力强度因子

Computing stress intensity factor using partition of unity enriched natural element method

基于单位分解的复杂系统分散自适应鲁棒控制设计

Decentralized Adaptive Robust Controller Design for Complex System Based on Partition of Unity

我们把这两种移动点方法应用到两个一维的对流扩散方程上，并把它们分别和迎风格式移动网格方法及等距剖分的一次单位分解方法相比较。

We apply these two moving particle methods to two one-dimensional convection-diffusion problems .

基于单位分解的一类组合系统自适应跟踪控制设计

Tracking control design for a class of interconnected systems based on partition of unity

具有可单位分解性质的谱容量

Spectral Capacities with the Property Decomposable Concerning Identity

基于局部多项式近似空间的单位分解方法的插值误差估计

Error Analysis of the Partition of Unity Method Based on Local Polynomial Approximation Space

基于单位分解技术，研究了交叠非匹配网格上双调和方程的协调有限元方法，给出了其整体协调有限元空间的构造，并对其有限元解的收敛性进行了分析证明。

The construcion and convergence analysis of a global conforming finite element method are given .

基于单位分解的新型有限元方法研究

Study on partition of unit FEM

使用单位分解积分，对传统的无单元伽辽金方法进行改进。

The element-free Galerkin method ( EFGM ) is improved with partition of unity quadrature ( PUQ ) .

提出了固体中短波传播数值模拟的单位分解有限元法。

A special integration scheme for partition of unity finite element method for short wave propagation in solids ;

最后，本文将单位分解无网格法运用于分析微带结构的散射问题。

Finally , the PUM based MLM is applied to analyze the electromagnetic scattering problems of the microstrip structure .

采用单位分解积分是一个很好的选择。5.本质边界条件的并行处理。

Partition of unity quadrature is a good choice for numerical quadrature in MNS . 5 . parallel enforcement of essential boundary condition .

移动单位分解方法的精度也比等距剖分的单位分解方法高很多，而且也比它要稳定。总的来说本文的数值实验说明了我们提出的移动点方法的有效性和优越性。

While the moving partition of unity method is more accurate than the equal distribution partition of unity method , and it is more stable .

在较弱的假设条件下，利用连续单位分解定理，讨论了G-凸空间中的重合点组定理。

In this paper , applying the continuous partition of unity theorem , we establish new systems of coincidence theorems in G-convex spaces under weaker assumptions .

第2和第3节分别简要介绍单位分解法和水平集法；

The partition of unity method ( PUM ) and Level Set Method ( LSM ) are briefly introduced in sections 2 and 3 , respectively .

本文我们针对上述两种无网格方法，提出移动有限点方法和移动单位分解方法，我们把它们都称为移动点方法。

In this paper , we propose the moving finite point method and moving partition of unity method . We call both of them moving particle method .

该方法利用单位分解法和有限覆盖建立节点形函数，使形函数的建立不受域内不连续的影响，方便了动态断裂力学问题的求解。

The method forms the shape function by the partition of unity and finite cover technology , so the shape functions cannot be effected by discontinuous in the domain .

虚节点法是一种新的基于单位分解理论的多边形有限元法。

A novel polygonal finite element method ( PFEM ), which is based on partition of unity , was proposed and named as virtual node method ( VNM ) .

另外，用弱形式求解控制微分方程时，单位分解积分为各种数值方法对弱形式的全域积分提供了统一的积分格式。给出非饱和土中热能传输和水分迁移的耦合控制微分方程。

In chapter 3 , issues regarding the numerical integration of the weak form are addressed . The system of partial differential equations governing the coupled processes of heat conduction and moisture transfer in unsaturated soils is presented .

通过改进再生核粒子逼近法，提出了最小二乘再生核法，并与单位分解法有机结合，应用到点模型的隐式曲面重建算法中，改善了重建效率。

A new least square reproducing kernel method is proposed based on reproducing kernel particle approximation and applied to implicit surface reconstruction from point clouds . It can improve the reconstruction efficiency by combining the partition of unity .

而单位分解方法的特点是不仅包含了有限元的知识，在解偏微分方程的时候，它比一般的有限元方法更有效。

And it appears to be computationally more simple and efficient . While the feature of partition of unity method is having the ability to include in the finite element space knowledge about the partial differential equation being solved .

实验结果表明，该并行计算方法可以有效地提高计算效率，对于单位分解函数集取线性函数时，计算中只需要较小的重叠度和较少的迭代次数即可满足实际需要。

The numerical results showed that the parallel computing method can improve computational efficiency . And when the unity partition function set takes the linear function , the calculation requires only small overlap and fewer iterations for the actual needs .

采用单位分解积分方案，其计算精度和收敛性均好于基于平均应变的点积分方案，但综合计算精度和计算效率考虑，则基于平均应变的点积分方案较为理想。

Considering both the accuracy and the efficiency , the point quadrature based on the average strain of Delaunay triangle is a better selection , though its convergence and accuracy are a little lower than the partition of unity quadrature method .

采用有限元形函数作为单位分解函数，位移间断用富集节点的附加自由度表示，建立了允许在单元内部位移非连续的局部富集公式以表征混凝土的开裂区域。

Using finite element shape functions as the partitions of unity , the discontinuous displacement is represented by extra degrees of freedom at enriched node . Local enrichment formulation based on dual overlapping meshes is developed to characterize fracture zone in concrete .

本文在单位分解法的理论基础上，应用裂纹尖端局部函数来扩展原有的数值流形方法的基函数，提出考虑裂纹尖端场的数值流形方法。

In this paper , based on the unit partition method , the basis functions of the NMM are expanded by using the local functions at the tip of the cracks , to formulate a numerical manifold method for crack tip fields .

本文基于流形思想，利用有限覆盖，单位分解等概念，引入建立在覆盖上的覆盖函数和具有紧支撑特性的单位分解函数，建立场量逼近的近似表达。

In the paper , by the use of concepts of finite cover and partition of unit in manifold ideas , cover function and partition of unit function are established on finite covers so that approximation of displacement field function is got .