Improving Lagrangian methods: toward an agent-particle based method

An agent-based modeling procedure is proposed in this paper in order to improve particles methods (like Smooth Particle Hydrodynamics, Vortex methods…) in the context of modeling and simulating physical or social systems described by partial differential equations. The procedure suggests, for avoiding some of the Lagrangian methods limitations, to replace the classical particle with an autonomous process -- an agent-particle: AP -- able to implement skills like vicinity perception, capacity of evaluating mutual contribution, testing complex behaviors… A complete description of concepts and tools that the AP-based method might use for limiting the combinatory complexity is first given; sending messages for symmetric contributions, quad-Lattices for neighbors searching, ray tracing and kd-tree-domains for handling obstacles… In a second part, a continuous convection-diffusion problem and a discrete animals aggregation are simulated to show what the AP-based method can bring to classical resolution schemes.