3D Shape Optimization based on Unstructured Triangle/Tetrahedral Mesh Deformation
Ruichao Ye, Maarten V. de Hoop · 2015
Summary We study a polyhedral representation of regional subsurface structures partitioned into unstructured tetrahedral mesh. The geomechanics-related discontinuities are adaptively represented as triangulated interior surfaces as seperators for blocky subdomains, or “shapes”, without asssumption on smoothness. We present a two-step framework conducting mesh deformation by evolving the interior surface based on the gradient flow derived from the Hausdorff distance between an initially guessed geometry and a target polyhedral representing the true geological structure, and then elastically deforming and modifying the volume mesh under element quality constraints. We implement a series of refinement and coarsening operations, allowing topological change, and introduce a polyhedra based level set function to retrack the interior surface, as a feedback from volume modification to surface mesh optimization, which deals with the contacting and breaking up problems.