An efficient data structure to solve front propagation problems

Olivier Bokanowski 1 Emiliano Cristiani 2 Hasnaa Zidani 2, 3, *
* Corresponding author
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées
Abstract : In this paper we develop a general efficient sparse storage technique suitable to coding front evolutions in d>= 2 space dimensions. This technique is mainly applied here to deal with deterministic target problems with constraints, and solve the associated minimal time problems. To this end we consider an Hamilton-Jacobi-Bellman equation and use an adapted anti-diffusive Ultra-Bee scheme. We obtain a general method which is faster than a full storage technique. We show that we can compute problems that are out of reach by full storage techniques (because of memory). Numerical experiments are provided in dimension d=2,3,4.
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Olivier Bokanowski, Emiliano Cristiani, Hasnaa Zidani. An efficient data structure to solve front propagation problems. Journal of Scientific Computing, Springer Verlag, 2010, 42 (2), pp.251--273. ⟨10.1007/s10915-009-9329-6⟩. ⟨inria-00273977v2⟩

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