228 research outputs found
Two semi-Lagrangian fast methods for Hamilton-Jacobi-Bellman equations
In this paper we apply the Fast Iterative Method (FIM) for solving general
Hamilton-Jacobi-Bellman (HJB) equations and we compare the results with an
accelerated version of the Fast Sweeping Method (FSM). We find that FIM can be
indeed used to solve HJB equations with no relevant modifications with respect
to the original algorithm proposed for the eikonal equation, and that it
overcomes FSM in many cases. Observing the evolution of the active list of
nodes for FIM, we recover another numerical validation of the arguments
recently discussed in [Cacace et al., SISC 36 (2014), A570-A587] about the
impossibility of creating local single-pass methods for HJB equations
Solving the Direction Field for Discrete Agent Motion
Models for pedestrian dynamics are often based on microscopic approaches
allowing for individual agent navigation. To reach a given destination, the
agent has to consider environmental obstacles. We propose a direction field
calculated on a regular grid with a Moore neighborhood, where obstacles are
represented by occupied cells. Our developed algorithm exactly reproduces the
shortest path with regard to the Euclidean metric.Comment: 8 pages, 4 figure
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