Amine Ammar

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: 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.

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.