Olivier Mercier

Research Scientist - Display Systems Research
Facebook Reality Labs

The Characteristic Mapping Method for the Linear Advection of Arbitrary Sets
SIAM Journal on Scientific Computing, 2020
Olivier Mercier
McGill University
Xi-Yuan Yin
McGill University
Jean-Christophe Nave
McGill University
We present a new numerical method for transporting arbitrary sets in a velocity field. The method computes a deformation mapping of the domain and advects particular sets by function composition with the map. This also allows for the transport of multiple sets at low computational cost. Our strategy is to separate the computation of short time advection from the storage and representation of long time deformation maps, employing appropriate grid resolution for each of these two parts. We show through numerical experiments that the resulting algorithm is accurate and exhibits significant reductions in computational time over other methods. Results are presented in two and three dimensions, and accuracy and efficiency are studied.
  title={The Characteristic Mapping Method for the Linear Advection of Arbitrary Sets},
  author={Mercier, Olivier and Yin, Xi-Yuan and Nave, Jean-Christophe},
  journal={SIAM Journal on Scientific Computing},