Geometry-Aware Computational Meshing in PETSc

Abstract Building on the framework for computational meshing in the PETSc library knepleykarpeev09,knepley2025, we have developed a tightly coupled geometry-discretization infrastructure, enabling geometric data to be used directly in simulation and analysis. We can create discretizations from common CAD geometry files, such as STEP and IGES, and enable many mesh transformations such as ``snap to'' refinement, where the geometric fidelity of the discretization increases with refinement. We also support direct manipulation of the underlying geometric data in order to enable optimization. This infrastructure maintains consistency between the geometry and discretization through transformations, which we illustrate through use cases.