Geometric low-rank tensors and their application for noise reduction of kinetic particle simulations (gemTENS)

Structure-preserving numerical algorithms are emerging tools for efficient andreliable computer simulations of complex systems in science andengineering.

In plasma physics, strucuture-preserving particle methods havebeen developed in recent years and are a very promising candidate forcutting-edge simulations of the kinetic equations to better understand thedynamics in the outer part of fusion energy devices.

However, the particlemethods suffer from intrinsic statistical noise and efficient noise-reductiontechniques are indispensable.A kinetic model describes the plasma in terms of a phase-space distributionfunction that depends on the three space variables, the three velocitycomponents and time, and is thus a rather high-dimensional model.

Thismotivates the proposed development of algorithms based on low-rank tensors, amathematical tool to efficently compress data in high-dimensions.It is the goal of the proposed work program to advance the mathematical fieldof structure-preserving low-rank methods and, in a second step, to apply thedevised methods as a noise reduction technique for particle simulations of thekinetic model in plasma physics.

The resulting numerical schemes will enableplasma physicists to simulate the region close to the wall in unprecedenteddetail.The team of this four year project consists of the applicant, associate professor with a strong background in scientific computing for high-dimensional problems and plasma physics applications, and a PhD student.