Adrien Leygue

TL;DR: The present text is the first available book describing the Proper Generalized Decomposition (PGD), and provides a very readable and practical introduction that allows the reader to quickly grasp the main features of the method.

TL;DR: A new paradigm in the field of simulation-based engineering sciences (SBES) to face the challenges posed by current ICT technologies is addressed, by combining an off-line stage in which the general PGD solution, the vademecum, is computed, and an on-line phase in which real-time response is obtained as a result of the queries.

TL;DR: The use of the PGD is illustrated in four problem categories related to computational rheology: the direct solution of the Fokker-Planck equation for complex fluids in configuration spaces of high dimension, the development of very efficient non-incremental algorithms for transient problems, and the solution of multidimensional parametric models obtained by introducing various sources of problem variability as additional coordinates.

TL;DR: The Proper Generalized Decomposition (PGD) method as mentioned in this paper is a technique for solving high-dimensional problems in science and engineering that has proven to be a significant step forward.

TL;DR: In-plane–out-of-plane separated representation of the involved fields within the context of the Proper Generalized Decomposition allows solving the fully 3D model by keeping a 2D characteristic computational complexity, without affecting the solvability of the resulting multidimensional model.