Geometric Particle-in-Cell Methods on Mapped Grids
Abstract
This work deals with reduced order methods for the solution of parametrized partial differential equations with moving features. Solutions of these class of equations are well known to be hard to approximate using linear reduced basis methods. We utilize results from optimal transportation theory to extend these methods. In particular, we present a novel registration method that is based on aligning solution features using an approximation of optimal transport maps.
BibTeX
@phdthesis{dissertation,
author = {Perse, Benedikt},
title = {Geometric Particle-in-Cell Methods on Mapped Grids},
year = {2021},
school = {Technische Universität München},
pages = {173},
language = {en},
abstract = {The geometric electromagnetic particle-in-cell (GEMPIC) framework provides the foundation for Vlasov-Maxwell solvers that preserve at the discrete level the non-canonical Hamiltonian structure. Preserving the structure of the kinetic equations enables stable numerical methods for long time simulations. In this dissertation, the GEMPIC framework is extended to curvilinear coordinates and perfect conductor boundary conditions. Several semi-implicit time integrators based either on a Hamiltonian splitting or on an antisymmetric splitting of the Poisson matrix are discussed and assessed regarding their conservation properties and computational efficiency.},
keywords = {},
note = {},
url = {https://mediatum.ub.tum.de/1611205},
doi = {},
}