Over the past decade, polyhedral meshing has been gaining popularity as a better alternative to tetrahedral meshing in certain applications. Within the class of polyhedral elements, Voronoi cells are particularly attractive thanks to their special geometric structure. What has been missing so far is a Voronoi mesher that is sufficiently robust to run automatically on complex models. In this video, we illustrate the main ideas behind the VoroCrust algorithm, highlighting both the theoretical guarantees and the practical challenges imposed by realistic inputs.
Leibniz International Proceedings in Informatics, LIPIcs
Abdelkader, Ahmed; Bajaj, Chandrajit L.; Ebeida, Mohamed S.; Mahmoud, Ahmed H.; Mitchell, Scott A.; Owens, John D.; Rushdi, Ahmad A.
We study the problem of decomposing a volume bounded by a smooth surface into a collection of Voronoi cells. Unlike the dual problem of conforming Delaunay meshing, a principled solution to this problem for generic smooth surfaces remained elusive. VoroCrust leverages ideas from α-shapes and the power crust algorithm to produce unweighted Voronoi cells conforming to the surface, yielding the first provably-correct algorithm for this problem. Given an ϵ-sample on the bounding surface, with a weak σ-sparsity condition, we work with the balls of radius δ times the local feature size centered at each sample. The corners of this union of balls are the Voronoi sites, on both sides of the surface. The facets common to cells on opposite sides reconstruct the surface. For appropriate values of ϵ, σ and δ, we prove that the surface reconstruction is isotopic to the bounding surface. With the surface protected, the enclosed volume can be further decomposed into an isotopic volume mesh of fat Voronoi cells by generating a bounded number of sites in its interior. Compared to state-of-the-art methods based on clipping, VoroCrust cells are full Voronoi cells, with convexity and fatness guarantees. Compared to the power crust algorithm, VoroCrust cells are not filtered, are unweighted, and offer greater flexibility in meshing the enclosed volume by either structured grids or random samples.
Liu, Jianfeng; Su, Qinglin; Moreno, Mariana; Laird, Carl D.; Nagy, Zoltan; Reklaitis, Gintaras
State estimation is a fundamental part of monitoring, control, and real-time optimization in continuous pharmaceutical manufacturing. For nonlinear dynamic systems with hard constraints, moving horizon estimation (MHE) can estimate the current state by solving a well-defined optimization problem where process complexities are explicitly considered as constraints. Traditional MHE techniques assume random measurement noise governed by some normal distributions. However, state estimates can be unreliable if noise is not normally distributed or measurements are contaminated with gross or systematic errors. To improve the accuracy and robustness of state estimation, we incorporate robust estimators within the standard MHE skeleton, leading to an extended MHE framework. The proposed MHE approach is implemented on two pharmaceutical continuous feeding–blending system (FBS) configurations which include loss-in-weight (LIW) feeders and continuous blenders. Numerical results show that our MHE approach is robust to gross errors and can provide reliable state estimates when measurements are contaminated with outliers and drifts. Moreover, the efficient solution of the MHE realized in this work, suggests feasible application of on-line state estimation on more complex continuous pharmaceutical processes.
The quality of automatic signal detections from sensor networks depends on individual detector trigger levels (TLs) from each sensor. The largely manual process of identifying effective TLs is painstaking and does not guarantee optimal configuration settings, yet achieving superior automatic detection of signals and ultimately, events, is closely related to these parameters. We present a Dynamic Detector Tuning (DDT) system that automatically adjusts effective TL settings for signal detectors to the current state of the environment by leveraging cooperation within a local neighborhood of network sensors. After a stabilization period, the DDT algorithm can adapt in near-real time to changing conditions and automatically tune a signal detector to identify (detect) signals from only events of interest. Our current work focuses on reducing false signal detections early in the seismic signal processing pipeline, which leads to fewer false events and has a significant impact on reducing analyst time and effort. This system provides an important new method to automatically tune detector TLs for a network of sensors and is applicable to both existing sensor performance boosting and new sensor deployment. With ground truth on detections from a local neighborhood of seismic sensors within a network monitoring the Mount Erebus volcano in Antarctica, we show that DDT reduces the number of false detections by 18% and the number of missed detections by 11% when compared with optimal fixed TLs for all sensors.
The objective of this paper is to present a local bounds preserving stabilized finite element scheme for hyperbolic systems on unstructured meshes based on continuous Galerkin (CG) discretization in space. A CG semi-discrete scheme with low order artificial dissipation that satisfies the local extremum diminishing (LED) condition for systems is used to discretize a system of conservation equations in space. The low order artificial diffusion is based on approximate Riemann solvers for hyperbolic conservation laws. In this case we consider both Rusanov and Roe artificial diffusion operators. In the Rusanov case, two designs are considered, a nodal based diffusion operator and a local projection stabilization operator. The result is a discretization that is LED and has first order convergence behavior. To achieve high resolution, limited antidiffusion is added back to the semi-discrete form where the limiter is constructed from a linearity preserving local projection stabilization operator. The procedure follows the algebraic flux correction procedure usually used in flux corrected transport algorithms. To further deal with phase errors (or terracing) common in FCT type methods, high order background dissipation is added to the antidiffusive correction. The resulting stabilized semi-discrete scheme can be discretized in time using a wide variety of time integrators. Numerical examples involving nonlinear scalar Burgers equation, and several shock hydrodynamics simulations for the Euler system are considered to demonstrate the performance of the method. For time discretization, Crank–Nicolson scheme and backward Euler scheme are utilized.