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Algorithmic Hexahedral Mesh Generation

Periodic Reporting for period 1 - AlgoHex (Algorithmic Hexahedral Mesh Generation)

Reporting period: 2020-02-01 to 2021-07-31

Digital geometry representations are nowadays a fundamental ingredient of many applications, as for instance CAD/CAM, fabrication, shape optimization, biomedical engineering, and numerical simulation. Among volumetric discretizations, the “holy grail” is a hexahedral mesh, i.e. a decomposition of the domain into conforming cube-like elements. For simulations, a hexahedral mesh offers accuracy and efficiency that cannot be obtained with alternatives like tetrahedral meshes, specifically when dealing with higher-order PDEs. So far, automatic hexahedral meshing of general volumetric domains is a long-standing, notoriously difficult, and open problem.

Our main goal is to develop algorithms for automatic hexahedral meshing of general volumetric domains that are (i) robust, (ii) scalable, and (iii) offer precise control on regularity, approximation error, and element sizing/anisotropy. Our approach is designed to replicate the success story of recent integer-grid map based algorithms for 2D quadrilateral meshing. The underlying methodology offers the essential global view on the problem that was lacking in previous attempts, mostly failing due to local considerations inducing global inconsistencies. Preliminary results of integer-grid map hexahedral meshing are encouraging and a breakthrough is in reach.
We made substantial progress regarding the task of correcting singularity graphs by developing the theory and an algorithm to turn arbitrary input frame fields into locally meshable ones. A preliminary version of our newly generated dataset, which specifically contains challenging inputs for hexahedral mesh generation, has been highly valuable in this research activity.
We made substantial progress regarding the task of correcting singularity graphs by developing the theory and an algorithm to turn arbitrary input frame fields into locally meshable ones. A preliminary version of our newly generated dataset, which specifically contains challenging inputs for hexahedral mesh generation, has been highly valuable in this research activity.