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. .