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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

1 Introduction

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

Physical systems are often modeled using partial differential equations (PDEs). The exact solution or closed form or analytical solutions to these PDEs is only available in special cases for specific geometries. Numerical methods can be used to approximate the exact solution in more general settings. The result of a numerical simulation is rarely exact. Nonetheless, computer-based numerical simulation has revolutionalized industrial product development throughout engineering disciplines. When comparing experiments and simulation with the aim of improving a simulation procedure to give more accurate results, it is necessary to understand the different sources of error. Figure 1.1 shows an overview of errors that occur at different stages of modeling and numerical simulation for a given numerical method.

Figure 1.1 Sources of error in simulation.

One of these numerical methods is called the “finite element method” (FEM). It is most commonly used in structural mechanics, although the field of application is much broader. The historic origins of the FEM cannot be uniquely determined. Mathematicians and engineers seemed to develop similar methods simultaneously which laid the foundations ...

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ISBN: 9780470667088Purchase Link