# partition of unity

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## partition of unity

[pär′tish·ən əv ′yü·nəd·ē]
(mathematics)
On a topological space X, this is a covering by open sets Uαwith continuous functions ƒαfrom X to [0,1], where each ƒαis zero on all but a finite number of the Uα, and the sum of all these ƒαat any point equals 1.
References in periodicals archive ?
These five indexes verify the condition of partition of unity, namely:
These five parameters verify the condition of fuzzy partition of unity, namely:
The vector components verify the partition of unity condition, namely:
There are many meshless methods, such as smoothed particle hydrodynamics method (SPH) [9, 10], the element-free Galerkin (EFG) method [11, 12], the collocation point method [13], the finite point method (FPM) [14, 15], reproducing kernel particle method (RKPM) [16], multiscale reproducing kernel particle method [17], the hp cloud method [18], the partition of unity finite element method [19, 20], generalized finite element method [21], meshless local Petrov-Galerkin method [22], least-square collocation meshless method [23], meshless weighted least-square method [24], complex variable meshless method (CVMM) [25, 26], and complex variable meshless manifold method (CVMMM) [27].
Babuska, "The partition of unity finite element method: basic theory and applications," Computer Methods in Applied Mechanics and Engineering, vol.
Buay Keke, a deputy principal for Kampala rebel based representative, rubbished partition of Unity state, referring to the commissioner's claim as lacking basis.
Once the multiscale implicit functions for each subdomain are constructed, function values at arbitrary position in overall domain can be evaluated by partition of unity method that calculates a reconstructed function value by weighted sum of local functions for neighbor subdomains.
We partition the given data into smaller subsets by using partition of unity (POU) to deal with large input data on computers with limited memory space.
The use of radial basis functions and the partition of unity techniques are presented;
Some methods coupling with the partition of unity method (PUM) [36, 37] have also been investigated in mechanical problems in recent years.
In this paper, a meshless radial basis function based on partition of unity method (RBF-PUM) is proposed to analyse 2D piezoelectric structures.
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