Abstract
This chapter addresses some advanced topics whose development remains work in progress. The first topic concerns the efficient treatment of non-linear models where standard strategies can fail for high-dimensional problems. The second topic concerns the use of advective stabilization when the involved fields are approximated in a separated form. Finally, we introduce a discrete form of the PGD solver, the one that we consider in computer implementations, that is then extended for considering a separated representation constructor based on residual minimization. Residual minimization is particularly suitable for addressing non-symmetric differential operators, for which the standard procedure described in the previous chapters can be inefficient (slow convergence and non-optimal representations).
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Chinesta, F., Keunings, R., Leygue, A. (2014). Advanced Topics. In: The Proper Generalized Decomposition for Advanced Numerical Simulations. SpringerBriefs in Applied Sciences and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-02865-1_6
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DOI: https://doi.org/10.1007/978-3-319-02865-1_6
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