Reduced basis methods for problems with moving features

Tobias Blickhan

2023-07-23 · PhD

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.

@phdthesis{dissertation,
	author = {Blickhan, Tobias Michael},
	
title = {Reduced basis methods for problems with moving features},
	year = {2024},
	school = {Technische Universität München},
	pages = {145},
	language = {en},
	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.},
	keywords = {parameterized partial differential equation, model order reduction, snapshot registration, optimal transport, transport-dominated problems},
	note = {},
	url = {https://mediatum.ub.tum.de/1726153},
	doi = {},
}