abstract

Author: Philipp137

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+In this project, we introduce the characteristic mapping method to address the complexity of high-
+dimensional kinetic equations, such as those involving ion-electron interactions in plasma fusion, by integrating mathematical modeling with high-performance computing. This semi-Lagrangian method achieves
+exponential resolution in linear time, revealing fine-scale details of the solutions and providing insights into
+the filamentation structure of plasmas. By employing reduced-order models, we significantly lower the
+numerical complexity of the computations. Our approach, which combines dimensionality reduction of
+sub-maps with refinement through map compositions via the solution operator, is innovative and paves the
+way for efficient evaluation of high-dimensional distribution functions across extended time intervals and
+multi-scale spatial domains. This project is designed to test the potential to enhance existing semi-Lagrangian
+techniques and advance our understanding of intricate local thermodynamic non-equilibrium phenomena in
+plasmas, with applications in magnetically confined fusion.
 
 ### Team: