99 research outputs found
JIGSAW-GEO (1.0): locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere
An algorithm for the generation of non-uniform, locally-orthogonal staggered
unstructured spheroidal grids is described. This technique is designed to
generate very high-quality staggered Voronoi/Delaunay meshes appropriate for
general circulation modelling on the sphere, including applications to
atmospheric simulation, ocean-modelling and numerical weather prediction. Using
a recently developed Frontal-Delaunay refinement technique, a method for the
construction of high-quality unstructured spheroidal Delaunay triangulations is
introduced. A locally-orthogonal polygonal grid, derived from the associated
Voronoi diagram, is computed as the staggered dual. It is shown that use of the
Frontal-Delaunay refinement technique allows for the generation of very
high-quality unstructured triangulations, satisfying a-priori bounds on element
size and shape. Grid-quality is further improved through the application of
hill-climbing type optimisation techniques. Overall, the algorithm is shown to
produce grids with very high element quality and smooth grading
characteristics, while imposing relatively low computational expense. A
selection of uniform and non-uniform spheroidal grids appropriate for
high-resolution, multi-scale general circulation modelling are presented. These
grids are shown to satisfy the geometric constraints associated with
contemporary unstructured C-grid type finite-volume models, including the Model
for Prediction Across Scales (MPAS-O). The use of user-defined mesh-spacing
functions to generate smoothly graded, non-uniform grids for multi-resolution
type studies is discussed in detail.Comment: Final revisions, as per: Engwirda, D.: JIGSAW-GEO (1.0): locally
orthogonal staggered unstructured grid generation for general circulation
modelling on the sphere, Geosci. Model Dev., 10, 2117-2140,
https://doi.org/10.5194/gmd-10-2117-2017, 201
Spherical layout implementation using centroidal voronoi tessellations
The 3D tree visualization faces multiple challenges: the election of an appropriate layout, the use of the interactions that make the data exploration easier and a metaphor that helps in the process of information understanding. A good combination of these elements will result in a visualization that effectively conveys the key features of a complex structure or system to a wide range of users and permits the analytical reasoning process. In previous works we presented the Spherical Layout, a technique for 3D tree visualization that provides an excellent base to achieve those key features. The layout was implemented using the Tri- Sphere algorithm, a method that discretized the spheres's surfaces with triangles to achieve a uniform distribution of the nodes. The goal of this work was centered in a new algorithm for the implementation of the Spherical layout; we called it the Spherical Centroidal Voronoi Tessella- tions (SCVT). In this paper we present a detailed description of this new implementation and a comparison with the TriSphere algorithm.VII Workshop Computación Gráfica, Imágenes y Visualización (WCGIV)Red de Universidades con Carreras en Informática (RedUNCI
Spherical Layout Implementation using Centroidal Voronoi Tessellations
The 3D tree visualization faces multiple challenges: the election of an
appropriate layout, the use of the interactions that make the data exploration
easier and a metaphor that helps in the process of information understanding. A
good combination of these elements will result in a visualization that
effectively conveys the key features of a complex structure or system to a wide
range of users and permits the analytical reasoning process. In previous works
we presented the Spherical Layout, a technique for 3D tree visualization that
provides an excellent base to achieve those key features. The layout was
implemented using the TriSphere algorithm, a method that discretized the
spheres's surfaces with triangles to achieve a uniform distribution of the
nodes. The goal of this work was centered in a new algorithm for the
implementation of the Spherical layout; we called it the Weighted Spherical
Centroidal Voronoi Tessellations (WSCVT). In this paper we present a detailed
description of this new implementation and a comparison with the TriSphere
algorithm
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Toward mixed-element meshing based on restricted Voronoi diagrams
In this paper we propose a method to generate mixed-element meshes (tetrahedra, triangular prisms, square pyramids) for B-Rep models. The vertices, edges, facets, and cells of the final volumetric mesh are determined from the combinatorial analysis of the intersections between the model components and the Voronoi diagram of sites distributed to sample the model. Inside the volumetric regions, Delaunay tetrahedra dual of the Voronoi diagram are built. Where the intersections of the Voronoi cells with the model surfaces have a unique connected component, tetrahedra are modified to fit the input triangulated surfaces. Where these intersections are more complicated, a correspondence between the elements of the Voronoi diagram and the elements of the mixedelement mesh is used to build the final volumetric mesh. The method which was motivated by meshing challenges encountered in geological modeling is demonstrated on several 3D synthetic models of subsurface rock volumes
Microstructural modeling and computational homogenization of the physically linear and nonlinear constitutive behavior of micro-heterogeneous materials
Engineering materials show a pronounced heterogeneity on a smaller scale that influences the macroscopic constitutive behavior. Algorithms for the periodic discretization of microstructures are presented. These are used within the Nonuniform Transformation Field Analysis (NTFA) which is an order reduction based nonlinear homogenization method with micro-mechanical background. Theoretical and numerical aspects of the method are discussed and its computational efficiency is validated
Spherical layout implementation using centroidal voronoi tessellations
The 3D tree visualization faces multiple challenges: the election of an appropriate layout, the use of the interactions that make the data exploration easier and a metaphor that helps in the process of information understanding. A good combination of these elements will result in a visualization that effectively conveys the key features of a complex structure or system to a wide range of users and permits the analytical reasoning process. In previous works we presented the Spherical Layout, a technique for 3D tree visualization that provides an excellent base to achieve those key features. The layout was implemented using the Tri- Sphere algorithm, a method that discretized the spheres's surfaces with triangles to achieve a uniform distribution of the nodes. The goal of this work was centered in a new algorithm for the implementation of the Spherical layout; we called it the Spherical Centroidal Voronoi Tessella- tions (SCVT). In this paper we present a detailed description of this new implementation and a comparison with the TriSphere algorithm.VII Workshop Computación Gráfica, Imágenes y Visualización (WCGIV)Red de Universidades con Carreras en Informática (RedUNCI
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MODELING CHAIN PACKING IN COMPLEX PHASES OF SELF-ASSEMBLED BLOCK COPOLYMERS
Block copolymer (BCP) melts undergo microphase seperation and form ordered soft matter crystals with varying domain shapes and symmetries. We study the con- nection between diblock copolymer molecular designs and thermodynamic selection of ordered crystals by modeling features of variable sub-domain geometry filled with individual blocks within non-canonical sphere-like and network phases that together with layered, cylindrical and canonical spherical phases forms “natural forms” of self- assembled amphiphilic soft matter at large. First, we present a model to revise our understanding of optimal Frank-Kasper sphere-like morphologies by advancing the- ory to account for varying domain volumes. We then develop generic approaches to quantify local changes to domain thickness or packing frustration using medial sets and show its application to morphologies with arbitrary domain topologies and sym- metries in both theoretical models and experimental data. We further use medial sets as a proxy for terminal boundaries of blocks within different domains and revise thermodynamic models of BCP assembly in the strong segregation limit. Finally, we use this revised model to study effect of elastic stiffness asymmetry on relaxing packing frustration experienced by BCPs in tubular and matrix domains leading to equilibrium double gyroid network morphology in diblock copolymers
VoroCrust: Voronoi Meshing Without Clipping
Polyhedral meshes are increasingly becoming an attractive option with
particular advantages over traditional meshes for certain applications. What
has been missing is a robust polyhedral meshing algorithm that can handle broad
classes of domains exhibiting arbitrarily curved boundaries and sharp features.
In addition, the power of primal-dual mesh pairs, exemplified by
Voronoi-Delaunay meshes, has been recognized as an important ingredient in
numerous formulations. The VoroCrust algorithm is the first provably-correct
algorithm for conforming polyhedral Voronoi meshing for non-convex and
non-manifold domains with guarantees on the quality of both surface and volume
elements. A robust refinement process estimates a suitable sizing field that
enables the careful placement of Voronoi seeds across the surface circumventing
the need for clipping and avoiding its many drawbacks. The algorithm has the
flexibility of filling the interior by either structured or random samples,
while preserving all sharp features in the output mesh. We demonstrate the
capabilities of the algorithm on a variety of models and compare against
state-of-the-art polyhedral meshing methods based on clipped Voronoi cells
establishing the clear advantage of VoroCrust output.Comment: 18 pages (including appendix), 18 figures. Version without compressed
images available on https://www.dropbox.com/s/qc6sot1gaujundy/VoroCrust.pdf.
Supplemental materials available on
https://www.dropbox.com/s/6p72h1e2ivw6kj3/VoroCrust_supplemental_materials.pd
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