Topology of Frame Field Design for Hex Meshing
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 hexahedr...
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Main Author | |
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Format | Journal Article |
Language | English |
Published |
10.11.2020
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Subjects | |
Online Access | Get full text |
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Summary: | 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 $CW$-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. |
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DOI: | 10.48550/arxiv.2011.05276 |