An adaptive sparse grid semi-Lagrangian scheme for first order Hamilton-Jacobi Bellman equations
An adaptive sparse grid semi-Lagrangian scheme for first order Hamilton-Jacobi Bellman equations
Dokument öffnen (2.8MB)Datum der Veröffentlichung
09.2012Verlag / herausgebende Einrichtung
Institut für Numerische Simulation (INS)Verlagsort
BonnMetadaten
Zur Langanzeige
Zitierbarer Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11937
Inhalt
We propose a semi-Lagrangian scheme using a spatially adaptive sparse grid to deal with non-linear time-dependent Hamilton-Jacobi Bellman equations. We focus in particular on front propagation models in higher dimensions which are related to control problems. We test the numerical efficiency of the method on several benchmark problems up to space dimension d = 8, and give evidence of convergence towards the exact viscosity solution. In addition, we study how the complexity and precision scale with the dimension of the problem.
Schlagwörter
Sparse grids, Hamilton-Jacobi Bellman equation, Front propagation, Semi-Lagrangian scheme, Adaptivity
Klassifikation (DDC)
510 Mathematik 518 Numerische AnalysisErstpublikation
https://ins.uni-bonn.de/publication/preprintsZugehörige Publikation(en)
https://doi.org/10.1007/s10915-012-9648-xReihe, Nummer
INS Preprints ; 1207Bokanowski, Olivier; Garcke, Jochen; Griebel, Michael; Klompmaker, Irene: An adaptive sparse grid semi-Lagrangian scheme for first order Hamilton-Jacobi Bellman equations. In: INS Preprints, 1207.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11937
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11937
@unpublished{handle:20.500.11811/11937,
author = {{Olivier Bokanowski} and {Jochen Garcke} and {Michael Griebel} and {Irene Klompmaker}},
title = {An adaptive sparse grid semi-Lagrangian scheme for first order Hamilton-Jacobi Bellman equations},
publisher = {Institut für Numerische Simulation (INS)},
year = 2012,
month = sep,
INS Preprints},
volume = 1207,
note = {We propose a semi-Lagrangian scheme using a spatially adaptive sparse grid to deal with non-linear time-dependent Hamilton-Jacobi Bellman equations. We focus in particular on front propagation models in higher dimensions which are related to control problems. We test the numerical efficiency of the method on several benchmark problems up to space dimension d = 8, and give evidence of convergence towards the exact viscosity solution. In addition, we study how the complexity and precision scale with the dimension of the problem.},
url = {https://hdl.handle.net/20.500.11811/11937}
}
author = {{Olivier Bokanowski} and {Jochen Garcke} and {Michael Griebel} and {Irene Klompmaker}},
title = {An adaptive sparse grid semi-Lagrangian scheme for first order Hamilton-Jacobi Bellman equations},
publisher = {Institut für Numerische Simulation (INS)},
year = 2012,
month = sep,
INS Preprints},
volume = 1207,
note = {We propose a semi-Lagrangian scheme using a spatially adaptive sparse grid to deal with non-linear time-dependent Hamilton-Jacobi Bellman equations. We focus in particular on front propagation models in higher dimensions which are related to control problems. We test the numerical efficiency of the method on several benchmark problems up to space dimension d = 8, and give evidence of convergence towards the exact viscosity solution. In addition, we study how the complexity and precision scale with the dimension of the problem.},
url = {https://hdl.handle.net/20.500.11811/11937}
}
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