1,716 research outputs found
Adaptive tetrahedral mesh generation by constrained Delaunay refinement
This paper discusses the problem of refining a constrained Delaunay tetrahedralization (CDT) for adaptive numerical simulation. A simple and efficient algorithm which makes use of the classical Delaunay refinement scheme is proposed. It generates an isotropic tetrahedral mesh corresponding to a sizing function which can be either user-specified or automatically derived from the input CDT. The quality of the produced meshes is guaranteed, i.e., most output tetrahedra have their circumradius-to-shortest-edge ratios bounded except those in the neighborhood of small input angles. Good mesh conformity can be obtained for smoothly changing sizing information. The algorithm has been implemented. Various examples are provided to illustrate its theoretical aspects as well as practical performance
Adaptive tetrahedral mesh generation by constrained delaunay refinement
This paper discusses the problem of refining a constrained Delaunay tetrahedralization (CDT) for adaptive numerical simulation. A simple and
efficient algorithm which makes use of the classical Delaunay refinement scheme is proposed. It generates an isotropic tetrahedral mesh corresponding to a sizing function which can be either user-specified or automatically derived from the input CDT. The quality of the produced meshes is guaranteed, i.e., most output tetrahedra have their circumradius-to-shortest-edge ratios bounded except those in the neighborhood of small input angles. Good mesh conformity can be obtained for smoothly changing sizing information. The algorithm has been implemented. Various examples are provided to illustrate its theoretical aspects as well as practical performance
Conforming restricted Delaunay mesh generation for piecewise smooth complexes
A Frontal-Delaunay refinement algorithm for mesh generation in piecewise
smooth domains is described. Built using a restricted Delaunay framework, this
new algorithm combines a number of novel features, including: (i) an
unweighted, conforming restricted Delaunay representation for domains specified
as a (non-manifold) collection of piecewise smooth surface patches and curve
segments, (ii) a protection strategy for domains containing curve segments that
subtend sharply acute angles, and (iii) a new class of off-centre refinement
rules designed to achieve high-quality point-placement along embedded curve
features. Experimental comparisons show that the new Frontal-Delaunay algorithm
outperforms a classical (statically weighted) restricted Delaunay-refinement
technique for a number of three-dimensional benchmark problems.Comment: To appear at the 25th International Meshing Roundtabl
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
One machine, one minute, three billion tetrahedra
This paper presents a new scalable parallelization scheme to generate the 3D
Delaunay triangulation of a given set of points. Our first contribution is an
efficient serial implementation of the incremental Delaunay insertion
algorithm. A simple dedicated data structure, an efficient sorting of the
points and the optimization of the insertion algorithm have permitted to
accelerate reference implementations by a factor three. Our second contribution
is a multi-threaded version of the Delaunay kernel that is able to concurrently
insert vertices. Moore curve coordinates are used to partition the point set,
avoiding heavy synchronization overheads. Conflicts are managed by modifying
the partitions with a simple rescaling of the space-filling curve. The
performances of our implementation have been measured on three different
processors, an Intel core-i7, an Intel Xeon Phi and an AMD EPYC, on which we
have been able to compute 3 billion tetrahedra in 53 seconds. This corresponds
to a generation rate of over 55 million tetrahedra per second. We finally show
how this very efficient parallel Delaunay triangulation can be integrated in a
Delaunay refinement mesh generator which takes as input the triangulated
surface boundary of the volume to mesh
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
Unstructured mesh algorithms for aerodynamic calculations
The use of unstructured mesh techniques for solving complex aerodynamic flows is discussed. The principle advantages of unstructured mesh strategies, as they relate to complex geometries, adaptive meshing capabilities, and parallel processing are emphasized. The various aspects required for the efficient and accurate solution of aerodynamic flows are addressed. These include mesh generation, mesh adaptivity, solution algorithms, convergence acceleration, and turbulence modeling. Computations of viscous turbulent two-dimensional flows and inviscid three-dimensional flows about complex configurations are demonstrated. Remaining obstacles and directions for future research are also outlined
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