SIAM Journal on Scientific Computing, Volume 42, Issue 3, Page A1663-A1685, January 2020.
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.

中文翻译：

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任意集合线性对流的特征映射方法

SIAM科学计算杂志，第42卷，第3期，第A1663-A1685页，2020年1月。
我们提出了一种在速度场中传输任意集合的新数值方法。该方法计算域的变形映射，并通过函数组成与映射平移特定的集合。这也允许以低的计算成本来运输多个集合。我们的策略是将短时对流的计算与长时变形图的存储和表示分开，对这两个部分的每一个都采用适当的网格分辨率。通过数值实验，我们证明了所得算法是准确的，并且与其他方法相比，计算时间显着减少。结果以二维和三维表示，并研究了准确性和效率。