Proper Generalized Decompositions An Introduction to Computer Implementation with Matlab
This book is intended to help researchers overcome the entrance barrier to Proper Generalized Decomposition (PGD), by providing a valuable tool to begin the programming task. Detailed Matlab Codes are included for every chapter in the book, in which the theory previously described is translated into...
| Main Authors: | , , |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer International Publishing
2016, 2016
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| Edition: | 1st ed. 2016 |
| Series: | SpringerBriefs in Applied Sciences and Technology
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Introduction
- 2 To begin with: PGD for Poisson problems
- 2.1 Introduction
- 2.2 The Poisson problem
- 2.3 Matrix structure of the problem
- 2.4 Matlab code for the Poisson problem
- 3 Parametric problems
- 3.1 A particularly challenging problem: a moving load as a parameter
- 3.2 The problem under the PGD formalism
- 3.2.1 Computation of S(s) assuming R(x) is known
- 3.2.2 Computation of R(x) assuming S(s) is known
- 3.3 Matrix structure of the problem
- 3.4 Matlab code for the influence line problem
- 4 PGD for non-linear problems
- 4.1 Hyperelasticity
- 4.2 Matrix structure of the problem
- 4.2.1 Matrix form of the term T2
- 4.2.2 Matrix form of the term T4
- 4.2.3 Matrix form of the term T6
- 4.2.4 Matrix form for the term T8
- 4.2.5 Matrix form of the term T9
- 4.2.6 Matrix form of the term T10
- 4.2.7 Final comments
- 4.3 Matlab code
- 5 PGD for dynamical problems
- 5.1 Taking initial conditions as parameters
- 5.2 Developing the weak form of the problem
- 5.3 Matrix form of the problem
- 5.3.1 Time integration of the equations of motion
- 5.3.2 Computing a reduced-order basis for the field of initial conditions
- 5.3.3 Projection of the equations onto a reduced, parametric basis
- 5.4 Matlab code
- References
- Index.