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Journal of Scientific Computing

Erschienen in:

10.03.2017

Numerical Investigation of a Class of Liouville Control Problems

verfasst von: Souvik Roy, Alfio Borzì

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2017

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Abstract

An accurate and efficient numerical scheme for solving a Liouville optimal control problem in the framework of the Pontryagin’s maximum principle (PMP) is presented. The Liouville equation models the time-evolution of a density function that may represent a distribution of non-interacting particles or a probability density. In this work, the purpose of the control is to maximize the measure of a target set at a given final time. In order to solve this problem, a high-order accurate conservative and positive preserving discretization scheme is investigated and a novel iterative optimization method is formulated that solves the PMP optimality condition without requiring differentiability with repsect to the control variable. Results of numerical experiments are presented that demonstrate the effectiveness of the proposed solution procedure.

Vorheriger Artikel On the Application of Reduced Basis Methods to Bifurcation Problems in Incompressible Fluid Dynamics

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Titel: Numerical Investigation of a Class of Liouville Control Problems
verfasst von: Souvik Roy
Alfio Borzì
Publikationsdatum: 10.03.2017
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2017
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-017-0410-2

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