Sparse Reconstruction of Multi-Dimensional Kinetic Distributions

arXiv (Cornell University)

Abstract

In the present work, we propose a novel method for reconstruction of multi-dimensional kinetic distributions, based on their representation as a mixture of Dirac delta functions. The representation is found as a solution of an optimization problem. Different target functionals are considered, with a focus on sparsity-promoting regularization terms. The proposed algorithm guarantees non-negativity of the distribution by construction, and avoids an exponential dependence of the computational cost on the dimensionality of the problem. Numerical comparisons with other classical methods for reconstruction of kinetic distributions are provided for model problems, and the role of the different parameters governing the optimization problem is studied.

Authors 3

1. Georgii Oblapenko Aachen Chair of Applied and Computational Mathematics

   RWTH Aachen University

   Affiliation as printed

   Chair of Applied and Computational Mathematics , RWTH Aachen , Schinkelstrasse 52 , 52062 Aachen , Germany

2. Manuel Torrilhon Aachen Chair of Applied and Computational Mathematics

   RWTH Aachen University

   Affiliation as printed

   Chair of Applied and Computational Mathematics , RWTH Aachen , Schinkelstrasse 52 , 52062 Aachen , Germany

3. Michaël Herty Aachen Institute of Geometry and Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Geometry and Applied Mechanics , RWTH Aachen , Templergraben 55 , 52062 Aachen , Germany