Geodesic
On a method of conservative remapping on hexahedral meshes
Matematičeskoe modelirovanie, Tome 20 (2008) no. 2, pp. 59-75

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A method of the conservative interpolation of physical parameters from the old structured hexahedral mesh to the new hexahedral mesh is considered. Conservative remapping is reduced to determining the volume of the overlapping figure between the old mesh cells and new mesh cells. The cell with the ruled faces is substituted for two dodecahedra with planar triangular faces. Thus, the interpolation is reduced to the problem of constructing the overlapping figure between two dodecahedra. For the underlying new mesh cell, the optimal algorithm of selecting the old mesh cells with nontrivial intersection is suggested. Interpolation error estimate is performed. Examples of remapping are presented. 
@article{MM_2008_20_2_a5,
     author = {B. N. Azarenok},
     title = {On a method of conservative remapping on hexahedral meshes},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {59--75},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2008_20_2_a5/}
}
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B. N. Azarenok. On a method of conservative remapping on hexahedral meshes. Matematičeskoe modelirovanie, Tome 20 (2008) no. 2, pp. 59-75. http://geodesic.mathdoc.fr/item/MM_2008_20_2_a5/