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In this paper, we present a new numerical method for advecting arbitrary sets in a vector field. The method computes a transformation of the domain instead of dealing with particular sets. We propose a way of decoupling the advection and representation steps of the computations, resulting in significant reductions in computational times over other methods while still guaranteeing accuracy. The decoupling also allows one to advect multiple sets at low computational cost, and makes the method highly parallelizable. Results are presented in two and three dimensions, and accuracy and efficiency are studied.

The Characteristic Mapping Method for the Linear Advection of Arbitrary Sets