ERC Starting Grant
Principal investigator: Prof. David Bommes, Institute of Computer Science
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.
The main goal of the AlgoHex team 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. The scientific 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.