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A Diffusion-Driven Characteristic Mapping Method for Particle Management
SIAM Journal on Scientific Computing  (IF2.373),  Pub Date : 2021-09-14, DOI: 10.1137/20m1364357
Xi-Yuan Yin, Linan Chen, Jean-Christophe Nave

SIAM Journal on Scientific Computing, Volume 43, Issue 5, Page A3155-A3183, January 2021.
We present a novel particle management method using the characteristic mapping framework. In the context of explicit evolution of parametrized curves and surfaces, the surface distribution of marker points created from sampling the parametric space is controlled by the area element of the parametrization function. As the surface evolves, the area element becomes uneven and the sampling suboptimal. In this method we maintain the quality of the sampling by precomposition of the parametrization with a deformation map of the parametric space. This deformation is generated by the velocity field associated to the diffusion process on the space of probability distributions and induces a uniform redistribution of the marker points. We also exploit the semigroup property of the heat equation to generate a submap decomposition of the deformation map which provides an efficient way of maintaining evenly distributed marker points on curves and surfaces undergoing extensive deformations.