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The incorporation of the handbook functions into the GFEM is done by employing the partition of unity method (PUM).
The Generalized Finite Element Method (GFEM) is a meshbased approach that can be considered as one instance of the Partition of Unity Method (PUM).
As a partition of unity method (PUM), the numerical manifold method (NMM) is capable of constructing global approximation by simply multiplying PU function with local approximation.
Additionally, we implement a partition of unity method in order to improve the computational efficiency of the radial basis function methods.
The ECDM is Partition of Unity Method (PUM) based and is a condensed FEM formulation through eliminating the enriched degree of freedoms (DoFs) for nonlinear fracture analysis.
Furthermore, implementation of the extended IGA which incorporates enrichment functions through the partition of unity method (PUM) is also presented, where several examples for both two-dimensional and three-dimensional fracture are illustrated.
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Partition of unity methods like the GFEM, rely on closed-form analytical enrichment functions.
RBF partition of unity methods (RBF PUM) allow for a significant sparsification of the linear system and lower the computational effort.
The partition-of-unity method is employed for the simulation of discrete cracking, where cracks can nucleate and propagate across finite elements at arbitrary locations and orientations.
The performance of the proposed partition-of-unity method is analyzed on several test examples for transient conduction radiation problems in two space dimensions.
One method of extending the color gamut of an R'G'B' system is to allow components to excurse below zero and above unity.
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