270,670 research outputs found
Problems on Polytopes, Their Groups, and Realizations
The paper gives a collection of open problems on abstract polytopes that were
either presented at the Polytopes Day in Calgary or motivated by discussions at
the preceding Workshop on Convex and Abstract Polytopes at the Banff
International Research Station in May 2005.Comment: 25 pages (Periodica Mathematica Hungarica, Special Issue on Discrete
Geometry, to appear
Distribution Iteration: A Robust Alternative to Source Iteration for Solving the Discrete Ordinates Radiation Transport Equations in Slab and XY- Geometries
The discrete ordinates method is widely used to solve the Boltzmann transport equation for neutral particle transport for many engineering applications. Source iteration is used to solve the discrete ordinates system of equations, but can be slow to converge in highly scattering problems. Synthetic acceleration techniques have been developed to address this shortcoming; however, recent research has shown synthetic acceleration to lose effectiveness or diverge for certain problems. LTC Wager introduced an alternative to source iteration and demonstrated it in slab geometry. Here the method is further developed, enhancing efficiency in various ways, and demonstrated in XY-geometry as well as slab geometry. It is shown to be efficient even for those problems for which diffusion-synthetic and transport-synthetic accelerations fail or are ineffective. The method has significant advantages for massively-parallel implementations
Algorithms and methods for discrete mesh repair
Computational analysis and design has become a fundamental part of product research, development, and manufacture in aerospace, automotive, and other industries. In general the success of the specific application depends heavily on the accuracy and consistency of the computational model used. The aim of this work is to reduce the time needed to prepare geometry for mesh generation. This will be accomplished by developing tools that semi-automatically repair discrete data. Providing a level of automation to the process of repairing large, complex problems in discrete data will significantly accelerate the grid generation process. The developed algorithms are meant to offer semi-automated solutions to complicated geometrical problems—specifically discrete mesh intersections and isolated boundaries. The intersection-repair strategy presented here focuses on repairing the intersection in-place as opposed to re-discretizing the intersecting geometries. Combining robust, efficient methods of detecting intersections and then repairing intersecting geometries in-place produces a significant improvement over techniques used in current literature. The result of this intersection process is a non-manifold, non-intersecting geometry that is free of duplicate and degenerate geometry. Results are presented showing the accuracy and consistency of the intersection repair tool. Isolated boundaries are a type of gap that current research does not address directly. They are defined by discrete boundary edges that are unable to be paired with nearby discrete boundary edges in order to fill the existing gap. In this research the method of repair seeks to fill the gap by extruding the isolated boundary along a defined vector so that it is topologically adjacent to a nearby surface. The outcome of the repair process is that the isolated boundaries no longer exist because the gap has been filled. Results are presented showing the precision of the edge projection and the advantage of edge splitting in the repair of isolated boundaries
A minimalistic approach for fast computation of geodesic distances on triangular meshes
The computation of geodesic distances is an important research topic in
Geometry Processing and 3D Shape Analysis as it is a basic component of many
methods used in these areas. In this work, we present a minimalistic parallel
algorithm based on front propagation to compute approximate geodesic distances
on meshes. Our method is practical and simple to implement and does not require
any heavy pre-processing. The convergence of our algorithm depends on the
number of discrete level sets around the source points from which distance
information propagates. To appropriately implement our method on GPUs taking
into account memory coalescence problems, we take advantage of a graph
representation based on a breadth-first search traversal that works
harmoniously with our parallel front propagation approach. We report
experiments that show how our method scales with the size of the problem. We
compare the mean error and processing time obtained by our method with such
measures computed using other methods. Our method produces results in
competitive times with almost the same accuracy, especially for large meshes.
We also demonstrate its use for solving two classical geometry processing
problems: the regular sampling problem and the Voronoi tessellation on meshes.Comment: Preprint submitted to Computers & Graphic
Geometry, Dynamics and Spectrum of Operators on Discrete Spaces (online meeting)
Spectral theory is a gateway to fundamental insights in geometry and mathematical physics. In recent years the study of spectral problems in discrete spaces has gained enormous momentum. While there are some relations to continuum spaces, fascinating new phenomena have been discovered in the discrete setting throughout the last decade. The goal of the workshop was to bring together experts reporting about the recent developments in a broad variety of dynamical or geometric models and to
reveal new connections and research directions
- …