Since separated representations allow one to circumvent the curse of dimensionality, one can consider model parameters, boundary conditions, initial conditions or geometrical parameters defining the computational domain, as extra-coordinates of the problem. Thus, standard models become multi-dimensional, but by solving them only once and offline using the PGD, the solution of the model is available for any choice of the parameters considered as extra-coordinates. This parametric solution can then be used online for different purposes, such as real time simulation, efficient optimization or inverse analysis, or simulation-based control. In this chapter, we illustrate the procedures for considering (a) model parameters, (b) constant and non-constant Dirichlet and Neumann boundary conditions, (c) initial conditions and (d) geometrical parameters, as extra-coordinates of a resulting multi-dimensional model.
KeywordsGeometrical parameters Material parameters Parametric boundary conditions Parametric model Parametric solution Proper Generalized Decomposition
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