1. A computer implemented method of coarsening a hexahedral mesh, comprising: identifying a coarsening region within the hexahedral mesh to be coarsened; inserting, with a computer, a boundary sheet of hexahedral elements into the hexahedral mesh around the coarsening region; identifying a plurality of internal sheets of hexahedral elements, of which at least a portion of each of the internal sheets passes through the coarsening region wherein the plurality of internal sheets comprise non-intersecting internal sheets; identifying columns of hexahedral elements defined by an intersection of the boundary sheet and the plurality of internal sheets; pairing at least a portion of the plurality of internal sheets based on adjacency of locations of the internal sheets; collapsing, with the computer, the columns of hexahedral elements to create extraction sheets of hexahedral elements contained within the coarsening region, wherein at least a portion of the columns are collapsed in alternating directions based on the pairing; and extracting, with the computer, the extraction sheets of hexahedral elements to coarsen the hexahedral mesh within the coarsening region.