arXiv subjects

Patrick Anderson

Publications and source records attributed to Patrick Anderson.

2 recordsLinked to original sources

arXiv2026

Intrusive versus non-intrusive reduced-order modeling of generalized Newtonian fluid flows

This study compares three reduced-order modeling (ROM) approaches for flow simulations of generalized Newtonian fluids described by the Carreau rheological model. All three methods rely on offline snapshot generation in the rheological parameter space using the full-order model (FOM), followed by a proper orthogonal decomposition (POD) of the snapshot matrix to obtain a reduced basis, but they differ in how they reconstruct the solution for new parameter values in the online phase. The three ROM approaches examined are: (i) intrusive Galerkin projection onto the reduced basis with full operator reassembly (ROM-FULL), (ii) intrusive hyper-reduced Galerkin projection using the discrete empirical interpolation method with GappyPOD for the nonlinear term (ROM-DEIM), and (iii) a non-intrusive interpolation approach using radial basis function interpolation (ROM-RBF). We demonstrate these three ROM approaches on two benchmark flows: a lid-driven cavity and a sphere settling in a closed container, spanning boundary-driven and force-driven flows. ROM-FULL achieves the highest accuracy but requires reassembling the full-order nonlinear operator during the online phase, whereas ROM-RBF is fully non-intrusive, and its accuracy is closely tied to data availability and deteriorates outside the training data range. ROM-DEIM offers a balance between efficiency and accuracy, even when data are sparse. The results provide guidelines for selecting an appropriate ROM strategy based on solver accessibility, computational efficiency, and desired accuracy.

physics.flu-dyn↗

arXiv2024

A Theory of Stabilization by Skull Carving

Accurate stabilization of facial motion is essential for applications in photoreal avatar construction for 3D games, virtual reality, movies, and training data collection. For the latter, stabilization must work automatically for the general population with people of varying morphology. Distinguishing rigid skull motion from facial expressions is critical since misalignment between skull motion and facial expressions can lead to animation models that are hard to control and can not fit natural motion. Existing methods struggle to work with sparse sets of very different expressions, such as when combining multiple units from the Facial Action Coding System (FACS). Certain approaches are not robust enough, some depend on motion data to find stable points, while others make one-for-all invalid physiological assumptions. In this paper, we leverage recent advances in neural signed distance fields and differentiable isosurface meshing to compute skull stabilization rigid transforms directly on unstructured triangle meshes or point clouds, significantly enhancing accuracy and robustness. We introduce the concept of a stable hull as the surface of the boolean intersection of stabilized scans, analogous to the visual hull in shape-from-silhouette and the photo hull from space carving. This hull resembles a skull overlaid with minimal soft tissue thickness, upper teeth are automatically included. Our skull carving algorithm simultaneously optimizes the stable hull shape and rigid transforms to get accurate stabilization of complex expressions for large diverse sets of people, outperforming existing methods.

cs.CV↗