Francisco Chinesta

TL;DR: This paper revisits a new model reduction methodology based on the use of separated representations, the so called Proper Generalized Decomposition—PGD, which allows to treat efficiently models defined in degenerated domains as well as the multidimensional models arising from multiddimensional physics or from the standard ones when some sources of variability are introduced in the model as extra-coordinates.

TL;DR: This work states thatKinetic theory models involving the Fokker-Planck equation can be accurately discretized using a mesh support using a reduced approximation basis within an adaptive procedure making use of an efficient separation of variables.

TL;DR: This paper revisits a powerful discretization technique, the Proper Generalized Decomposition—PGD, illustrating its ability for solving highly multidimensional models.

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: This work presents a new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids using separated representations and tensor product approximations basis for treating transient models.