Integer-Sheet-Pump Quantization for Hexahedral Meshing

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dc.contributor.authorBrückler, Hendriken_US
dc.contributor.authorBommes, Daviden_US
dc.contributor.authorCampen, Marcelen_US
dc.contributor.editorHu, Ruizhenen_US
dc.contributor.editorLefebvre, Sylvainen_US
dc.date.accessioned2024-06-20T07:54:52Z
dc.date.available2024-06-20T07:54:52Z
dc.date.issued2024
dc.description.abstractSeveral state-of-the-art algorithms for semi-structured hexahedral meshing involve a so called quantization step to decide on the integer DoFs of the meshing problem, corresponding to the number of hexahedral elements to embed into certain regions of the domain. Existing reliable methods for quantization are based on solving a sequence of integer quadratic programs (IQP). Solving these in a timely and predictable manner with general-purpose solvers is a challenge, even more so in the open-source field. We present here an alternative robust and efficient quantization scheme that is instead based on solving a series of continuous linear programs (LP), for which solver availability and efficiency are not an issue. In our formulation, such LPs are used to determine where inflation or deflation of virtual hexahedral sheets are favorable. We compare our method to two implementations of the former IQP formulation (using a commercial and an open-source MIP solver, respectively), finding that (a) the solutions found by our method are near-optimal or optimal in most cases, (b) these solutions are found within a much more predictable time frame, and (c) the state of the art run time is outperformed, in the case of using the open-source solver by orders of magnitude.en_US
dc.description.number5
dc.description.sectionheadersMeshing
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume43
dc.identifier.doi10.1111/cgf.15131
dc.identifier.issn1467-8659
dc.identifier.pages13 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.15131
dc.identifier.urihttps://diglib.eg.org/handle/10.1111/cgf15131
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectKeywords: T-mesh, hexahedral mesh, volume mesh, integer optimization, block decomposition, base complex, hex sheet
dc.subjectT
dc.subjectmesh
dc.subjecthexahedral mesh
dc.subjectvolume mesh
dc.subjectinteger optimization
dc.subjectblock decomposition
dc.subjectbase complex
dc.subjecthex sheet
dc.titleInteger-Sheet-Pump Quantization for Hexahedral Meshingen_US
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