Robust Polyhedral Meshing
Abstract not provided.
Publications
A Novel Voronoi Piecewise Approach to Solve Stochastic PDEs
Abstract not provided.
All-quad meshing without cleanup
CAD Computer Aided Design
We present an all-quad meshing algorithm for general domains. We start with a strongly balanced quadtree. In contrast to snapping the quadtree corners onto the geometric domain boundaries, we move them away from the geometry. Then we intersect the moved grid with the geometry. The resulting polygons are converted into quads with midpoint subdivision. Moving away avoids creating any flat angles, either at a quadtree corner or at a geometry–quadtree intersection. We are able to handle two-sided domains, and more complex topologies than prior methods. The algorithm is provably correct and robust in practice. It is cleanup-free, meaning we have angle and edge length bounds without the use of any pillowing, swapping, or smoothing. Thus, our simple algorithm is fast and predictable. This paper has better quality bounds, and the algorithm is demonstrated over more complex domains, than our prior version.
Ensemble Grouping strategies for embedded Stochastic Collocation
Abstract not provided.
POF-Darts: Geometric adaptive sampling for probability of failure
Reliability Engineering and System Safety
We introduce a novel technique, POF-Darts, to estimate the Probability Of Failure based on random disk-packing in the uncertain parameter space. POF-Darts uses hyperplane sampling to explore the unexplored part of the uncertain space. We use the function evaluation at a sample point to determine whether it belongs to failure or non-failure regions, and surround it with a protection sphere region to avoid clustering. We decompose the domain into Voronoi cells around the function evaluations as seeds and choose the radius of the protection sphere depending on the local Lipschitz continuity. As sampling proceeds, regions uncovered with spheres will shrink, improving the estimation accuracy. After exhausting the function evaluation budget, we build a surrogate model using the function evaluations associated with the sample points and estimate the probability of failure by exhaustive sampling of that surrogate. In comparison to other similar methods, our algorithm has the advantages of decoupling the sampling step from the surrogate construction one, the ability to reach target POF values with fewer samples, and the capability of estimating the number and locations of disconnected failure regions, not just the POF value. We present various examples to demonstrate the efficiency of our novel approach.
Triangulation / Voronoi Cell Based RKPM
Abstract not provided.
Disk Density Tuning of a Maximal Random Packing
Computer Graphics Forum
We introduce an algorithmic framework for tuning the spatial density of disks in a maximal random packing, without changing the sizing function or radii of disks. Starting from any maximal random packing such as a Maximal Poisson-disk Sampling (MPS), we iteratively relocate, inject (add), or eject (remove) disks, using a set of three successively more-aggressive local operations. We may achieve a user-defined density, either more dense or more sparse, almost up to the theoretical structured limits. The tuned samples are conflict-free, retain coverage maximality, and, except in the extremes, retain the blue noise randomness properties of the input. We change the density of the packing one disk at a time, maintaining the minimum disk separation distance and the maximum domain coverage distance required of any maximal packing. These properties are local, and we can handle spatially-varying sizing functions. Using fewer points to satisfy a sizing function improves the efficiency of some applications. We apply the framework to improve the quality of meshes, removing non-obtuse angles; and to more accurately model fiber reinforced polymers for elastic and failure simulations.
Steiner Point Reduction in Planar Delaunay Meshes
Abstract not provided.
VPS: Voronoi Piecewise Surrogate Models for High-Dimensional Data Fitting
Abstract not provided.
Recursive k-d Darts for Exploring High-Dimensional Spaces
Abstract not provided.
All-Hex Meshing of Multiple-Region Domains without Cleanup
Procedia Engineering
In this paper, we present a new algorithm for all-hex meshing of domains with multiple regions without post-processing cleanup. Our method starts with a strongly balanced octree. In contrast to snapping the grid points onto the geometric boundaries, we move points a slight distance away from the common boundaries. Then we intersect the moved grid with the geometry. This allows us to avoid creating any flat angles, and we are able to handle two-sided regions and more complex topologies than prior methods. The algorithm is robust and cleanup-free; without the use of any pillowing, swapping, or smoothing. Thus, our simple algorithm is also more predictable than prior art.
Recursive Spoke Darts: Local Hyperplane Sampling for Delaunay and Voronoi Meshing in Arbitrary Dimensions
Procedia Engineering
We introduce Recursive Spoke Darts (RSD): a recursive hyperplane sampling algorithm that exploits the full duality between Voronoi and Delaunay entities of various dimensions. Our algorithm abandons the dependence on the empty sphere principle in the generation of Delaunay simplices providing the foundation needed for scalable consistent meshing. The algorithm relies on two simple operations: line-hyperplane trimming and spherical range search. Consequently, this approach improves scalability as multiple processors can operate on different seeds at the same time. Moreover, generating consistent meshes across processors eliminates the communication needed between them, improving scalability even more. We introduce a simple tweak to the algo- rithm which makes it possible not to visit all vertices of a Voronoi cell, generating almost-exact Delaunay graphs while avoiding the natural curse of dimensionality in high dimensions.
Some Test Problems and Results in Assessing Methods for Calculating Low Probabilities of Failure
Abstract not provided.
Efficient Probability of Failure Calculations for QMU using Computational Geometry LDRD 13-0144 Final Report
This SAND report summarizes our work on the Sandia National Laboratory LDRD project titled "Efficient Probability of Failure Calculations for QMU using Computational Geometry" which was project #165617 and proposal #13-0144. This report merely summarizes our work. Those interested in the technical details are encouraged to read the full published results, and contact the report authors for the status of the software and follow-on projects.
Unleashing the Power of Voronoi Decompositions in low and high dimensions
Abstract not provided.
POF-Darts: Geometric Adaptive Sampling for Probability of Failure
SIAM Journal on Uncertainty Quantification
Abstract not provided.
Delaunay quadrangulation by two-coloring vertices - extended version with quad-quality proofs appendix
Abstract not provided.
Improved Poisson-disk Sampling for Meshing Applications
Abstract not provided.
Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis :
The Dakota (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a exible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quanti cation with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a exible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a user's manual for the Dakota software and provides capability overviews and procedures for software execution, as well as a variety of example studies.
Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis version 6.0 theory manual
The Dakota (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a exible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quanti cation with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a exible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quanti cation, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.
Tuning the Discrete Density of a Random Disk Packing by Injection and Ejection
Abstract not provided.
Delaunay Quadrangulation via Poisson Disk Sampling
Abstract not provided.
Improving Spatial Coverage while Preserving Blue Noise
Abstract not provided.
Balloon Darts: Estimating the Volume of the Union of d-Balls with Spoke Samples
Abstract not provided.
Advancing Front for Efficient Blue Noise Sampling Across Various Dimensions
Abstract not provided.
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