Node Distribution for Numerical Methods with Monte Carlo Simulation

H. Zhang and A.V. Smirnov (USA)


Monte Carlo simulation, node generation, mesh generation, constrained Delaunay triangulation


Computational domains are represented in meshless nu merical methods by nodes, or in mesh-based methods by elements connected by nodes. Good nodal distribution is essential for the convergence of numerical methods. In our study a new approach based on Monte Carlo simulation is proposed for node distribution. Surface or volume do mains to be discretized are treated as atomic systems, and mesh nodes are considered as interacting particles. Par ticles are inserted/removed into/from the system, as well as displaced, using Grand Canonical Monte Carlo method. With energy minimization by the Monte Carlo simulation, a good number of particles, i.e. nodes, are distributed with desired separation from each other. The nodal sepa ration is controlled by a predefined node spacing function. For mesh-based numerical methods, well-shaped triangu lar mesh elements can then be generated by connecting the nodes with constrained Delaunay methods. The algorithm works in an almost identical way for both 2D and 3D cases.

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