Project description
Robust and scalable algorithms for automatic hexahedral mesh generation
Geometric representations of objects are vital components of many applications such as computer-aided design, biomedical engineering and numerical simulation. The most sought-after representations are hexahedral meshes as they offer a level of accuracy and efficiency that cannot be obtained with other alternatives. However, automatic hexahedral meshing of general volumetric domains has proven to be a persistently difficult problem. The EU-funded AlgoHex project intends to solve this problem by replicating the success story of recent integer-grid map-based algorithms for 2D quadrilateral meshing. To do this, it will develop robust and scalable algorithms for automatic hexahedral mesh generation that offer precise control on regularity, approximation error and element sizing. The project’s approach offers a previously lacking global perspective on the problem.
Objective
"Digital geometry representations are nowadays a fundamental ingredient of many applications, as for instance CAD/CAM, fabrication, shape optimization, bio-medical engineering and numerical simulation. Among volumetric discretizations, the ""holy grail"" are hexahedral meshes, i.e. a decomposition of the domain into conforming cube-like elements. For simulations they offer 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. Preliminary results of integer-grid map hexahedral meshing are promising and a breakthrough is in reach. We identified five challenges that need to be addressed in order to reach practically sufficient hexahedral mesh generation. These challenges have partly been resolved in 2D, however, the solutions do not generalize to 3D due to the increased mathematical complexity of 3D manifolds. Nevertheless, with our experience in developing and evaluating the 2D techniques, we identified the key properties that are necessary for success and accordingly propose novel volumetric counterparts that will be developed in the AlgoHex project."
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Funding Scheme
ERC-STG - Starting GrantHost institution
3012 Bern
Switzerland