MUltiscale and treFFtz for numerIcal traNsport – MUFFIN
In many applications, one is faced with the problem of solving numerically a set of transport equations, also called kinetic equations in this document. The huge difficulty attached to this task is that it may be computationally exhausting, mainly because of the high dimension and of the multi-scale nature of the model (with strong gradients/filamentation, or with boundary layers/jump in the coefficients). Therefore one is forced to admit that the numerical solution of transport/kinetic equations is a bottleneck for advanced modeling and simulation in applied multi-physics sciences. Some recent references we are interested in are in the context of supercomputing and in the context of computational magnetized.
The objective of the proposed research is to explore and optimize original computational and numerical scenarios for multi-scale and high dimensional transport codes, with priority applications in plasma physics. It is at the frontier of computing and numerical analysis and intends to reduce the computational burden in the context of intensive calculation. The general idea is to exploit the local/global information (this typically is a multi-scale information about the local equilibria) present in the physics or in the partial differential equations, to introduce this information in the design of advanced approximation strategies and design and test numerical codes in order to validate the strategy. The nature of the implementation issues (implementation per se, CPU requirements, memory requirements, linear algebra issues for implicit schemes, compatibility with modern architectures, …) can be revealed only by implementing the methods and testing on challenging physical configurations (issued from magnetized and non magnetized plasma physics in our case). Within this project, the physical configurations will be taken mainly from the modeling of plasma with or without magnetic field. Our interest in these methods is because they introduce a priori information in the discretization procedure to save computational resources. Preliminary publications detailed afterward assess that the scientific foundations of the methods/algorithms are now solid enough so that numerical analysis and implementation can be advanced in parallel.
Monsieur Bruno Despres (Laboratoire Jacques-Louis Lions)
The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.
IMT Institut de Mathématiques de Toulouse
LMJL LABORATOIRE DE MATHEMATIQUES JEAN LERAY
LJLL Laboratoire Jacques-Louis Lions
Help of the ANR 408,569 euros
Beginning and duration of the scientific project: November 2019 - 48 Months