Abstract: Systems and methods are provided for modeling physical objects. Volumetric modeling operations are implemented with implicit surfaces on graphics processing units (GPUs) for Finite Element Analyses. For example, a number of implicit surfaces associated with signed distance fields are determined, and locality information associated with the implicit surfaces is obtained. Whether to blend the implicit surfaces is determined based at least in part on the locality information.

Abstract: Systems and methods are provided for quadrilateral mesh generation. The system includes one or more data processors and a non-transitory computer-readable storage medium. The data processors are configured to: receive a geometric structure representing a physical object; determine a directional field; determine a size field; select one or more locations from a region of the geometric structure, the locations being associated with local data; and generate one or more quadrilateral mesh elements based at least in part on the directional field, the size field, and the local data. The non-transitory computer-readable storage medium is configured to store data related to the structure, data related to the directional field, data related to the size field, and the local data.