The Hexahedralization Sensation

Automatic conversion of computer aided drafting (CAD) geometry to computational grids appropriate for high fidelity hypersonic analysis is needed. With respect to grid quality, the output must be purely hexahedral and C2 continuous, even at extraordinary vertices. To accomplish this, a pipeline of local and global CAD repair algorithms will feed into a feature-preserving quadrangulation module with optional adaptive surface refinement. Catmull-Clark subdivision surfaces will be iteratively aligned to the quadrilateral surface meshes to provide a lightweight parametric representation. Recent advances from the computer graphics community will be employed to assure C2 continuity at extraordinary vertices. These techniques map a C2 continuous polynomial onto the subdivision surface with a C2 continuous compact weight function. The result will be projected back into the UV space of the input CAD to enable geometric surface sensitivities. Proven quadrangulation algorithms will then be extended to 3D hexahedralization to enable the automatic generation of purely hexahedral volumetric grids. Similarly, 3D subdivision volumes will map hexahedra to continuous, lightweight parametric representations. An additional library will be created to discretize the parametric grids and push them directly into processor memory. Bypassing the hard drive in this way is essential for parallel scalability to billions of grid cells.