An adaptive sparse grid semi-lagrangian scheme for first order Hamilton-Jacobi Bellman equations

Olivier Bokanowski 1, 2 Jochen Garcke 3 Michael Griebel 3 Irene Klompmaker 4
1 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
ENSTA ParisTech UMA - Unité de Mathématiques Appliquées, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, INRIA Saclay - Ile de France, Polytechnique - X, Univ. Paris-Saclay, ENSTA ParisTech - École Nationale Supérieure de Techniques Avancées, CNRS : UMR7641
Abstract : 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.
Document type :
Journal articles
Journal of Scientific Computing, Springer Verlag (Germany), 2013, 55, pp. 575-605. <10.1007/s10915-012-9648-x>


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Submitted on : Friday, October 12, 2012 - 1:08:49 PM
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Olivier Bokanowski, Jochen Garcke, Michael Griebel, Irene Klompmaker. An adaptive sparse grid semi-lagrangian scheme for first order Hamilton-Jacobi Bellman equations. Journal of Scientific Computing, Springer Verlag (Germany), 2013, 55, pp. 575-605. <10.1007/s10915-012-9648-x>. <hal-00741178>

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