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Partition of Unity Methods
book

Partition of Unity Methods

by Stéphane P. A. Bordas, Alexander Menk, Sundararajan Natarajan
October 2023
Intermediate to advanced content levelIntermediate to advanced
368 pages
12h 57m
English
Wiley
Content preview from Partition of Unity Methods

3 Partition of Unity Revisited

Stéphane P. A. Bordas1, Alexander Menk2, and Sundararajan Natarajan3

1 University of Luxembourg, Luxembourg, UK2 Robert Bosch GmbH, Germany3 Indian Institute of Technology Madras, India

The previous chapter provided a first introduction to the concept of enrichment and introduced some key issues related to its use within a finite element framework. The goal of the present chapter is to take the concept one step further and analyze more in depth the notions of completeness, partition of unity, mesh-geometry interaction, and imposition of boundary conditions.

3.1 Completeness, Consistency, and Reproducing Conditions

The notion of partition of unity is easily introduced by defining the completeness of approximations, which is expressed in terms of the highest order of the polynomials that can be represented exactly.

Definition 1 [Reproducing condition] Let p be a function defined over normal upper Omega and a set of approximating functions upper N Subscript upper J defined over a set of nodes bold x Subscript upper J such that . The ’s reproduce on , if and only if:

(3.1)

For example, if the approximation is able to ...

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ISBN: 9780470667088Purchase Link