In the past decade frame fields have emerged as a promising approach for generating hexahedral meshes for CFD and CAE applications. One important problem asks for construction of a boundary aligned frame field with prescribed singularity constraints that correspond to a valid hexahedral mesh. We give a necessary and sufficient condition in terms of solutions to a system of monomial equations whose variables are in the binary octahedral group  . Along the way we look at frame field design from an algebraic topological perspective, proving various results, some known, some new.
In the past decade frame fields have emerged as a promising approach for generating hexahedral meshes for CFD and CAE applications. One important problem asks for construction of a boundary-aligned frame field with prescribed singularity constraints over a volume that corresponds to a valid hexahedral mesh. We give a necessary and sufficient condition in terms of solutions to a system of monomial equations with variables in the binary octahedral group when a boundary frame field and singularity graph have been fixed. This is phrased with respect to general cellular decompositions of the volume, which allows some flexibility in simplifying these systems . Along the way we look at frame field design from an algebraic topological perspective, proving various results, some known, some new.
R
boundary aligned
boundary-aligned
R
that correspond
over a volume that corresponds
R
whose variables are
with variables
A
when a boundary frame field and singularity graph have been fixed. This is phrased with respect to general cellular decompositions of the volume, which allows some flexibility in simplifying these systems