Three viewpoints on null-collision Monte Carlo algorithms

El Hafi, Mouna ; Blanco, Stephane ; Dauchet, Jérémi ; Fournier, Richard ; Galtier, Mathieu ; Ibarrart, Loris ; Tregan, Jean-Marc ; Villefranque, Najda

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<p align=justify>In 2013, Galtier et al. [1] theoretically revisited a numerical trick that had been used since the very beginning of linear-transport Monte-Carlo simulation: introducing "null" scatterers into a heterogeneous field to make it virtually homogeneous. The rigorous connection between null-collision algorithms and integral formulations of the radiative transfer equation led to null-collision algorithms being used in distinct contexts, from atmospheric or combustion sciences to computer graphics, addressing questions that may strongly depart from the initial objective of handling heterogeneous fields (handling large spectroscopic databases, non-linearly coupling radiation with other physics). We briefly describe here some of this research and we classify it by proposing three alternative viewpoints on the very same null-collision concept: an intuitive, physical point of view, called similitude; a viewpoint built on the probability theory, where the null-collision method is seen as rejection sampling; and a more formal writing where the nonlinear exponential function is expanded into an infinite sum of linear terms. By formulating the null-collision concept under three distinct formalisms, our intention is to increase the reader's awareness of its flexibility.The idea defended and illustrated in this paper is that the ability to explore null-collision algorithms under their different forms has often led to a broadening of the solution space when facing difficult problems, including ones where the Monte Carlo method was consensually considered inapplicable.</p>
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