33,987 research outputs found
Higher-quality tetrahedral mesh generation for domains with small angles by constrained Delaunay refinement
Algorithms for generating Delaunay tetrahedral meshes
have difficulty with domains whose boundary polygons meet at small angles.
The requirement that all tetrahedra be Delaunay often forces
mesh generators to overrefine near small domain angles---that is,
to produce too many tetrahedra, making them too small.
We describe a provably good algorithm that generates meshes that
are constrained Delaunay triangulations, rather than purely Delaunay.
Given a piecewise linear domain free of small angles,
our algorithm is guaranteed to construct a mesh in which every tetrahedron has
a radius-edge ratio of or better.
This is a substantial improvement over the usual bound of ;
it is obtained by relaxing the conditions in which
boundary triangles are subdivided.
Given a domain with small angles,
our algorithm produces a mesh in which the quality guarantee is
compromised only in specific places near small domain angles.
We prove that most mesh edges have lengths proportional to
the domain's minimum local feature size;
the exceptions span small domain angles.
Our algorithm tends to generate meshes with fewer tetrahedra than
purely Delaunay methods because
it uses the constrained Delaunay property, rather than vertex insertions,
to enforce the conformity of the mesh to the domain boundaries.
An implementation demonstrates that our algorithm does not overrefine near
small domain angles
Decoupling method for parallel Delaunay two-dimensional mesh generation
Parallel mesh generation procedures that are based on geometric domain decompositions require the permanent separators to be of good quality (in terms of their angles and length), in order to maintain the mesh quality. The Medial Axis Domain Decomposition, an innovative geometric domain decomposition procedure that addresses this problem, is introduced. The Medial Axis domain decomposition is of high quality in terms of the formed angles, and provides separators of small size, and also good work-load balance. It presents for the first time a decomposition method suitable for parallel meshing procedures that are based on geometric domain decompositions.;The Decoupling Method for parallel Delaunay 2D mesh generation is a highly efficient and effective parallel procedure, able to generate billions of elements in a few hundred of seconds, on distributed memory machines. Our mathematical formulation introduces the notion of the decoupling path, which guarantees the decoupling property, and also the quality and conformity of the Delaunay submeshes. The subdomains are meshed independently, and as a result, the method eliminates the communication and the synchronization during the parallel meshing. A method for shielding small angles is introduced, so that the decoupled parallel Delaunay algorithm can be applied on domains with small angles. Moreover, I present the construction of a sizing function, that encompasses an existing sizing function and also geometric features and small angles. The decoupling procedure can be used for parallel graded Delaunay mesh generation, controlled by the sizing function
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
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
3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries
Recent advances in electron microscopy have enabled the imaging of single
cells in 3D at nanometer length scale resolutions. An uncharted frontier for in
silico biology is the ability to simulate cellular processes using these
observed geometries. Enabling such simulations requires watertight meshing of
electron micrograph images into 3D volume meshes, which can then form the basis
of computer simulations of such processes using numerical techniques such as
the Finite Element Method. In this paper, we describe the use of our recently
rewritten mesh processing software, GAMer 2, to bridge the gap between poorly
conditioned meshes generated from segmented micrographs and boundary marked
tetrahedral meshes which are compatible with simulation. We demonstrate the
application of a workflow using GAMer 2 to a series of electron micrographs of
neuronal dendrite morphology explored at three different length scales and show
that the resulting meshes are suitable for finite element simulations. This
work is an important step towards making physical simulations of biological
processes in realistic geometries routine. Innovations in algorithms to
reconstruct and simulate cellular length scale phenomena based on emerging
structural data will enable realistic physical models and advance discovery at
the interface of geometry and cellular processes. We posit that a new frontier
at the intersection of computational technologies and single cell biology is
now open.Comment: 39 pages, 14 figures. High resolution figures and supplemental movies
available upon reques
Boundary-Conforming Finite Element Methods for Twin-Screw Extruders using Spline-Based Parameterization Techniques
This paper presents a novel spline-based meshing technique that allows for
usage of boundary-conforming meshes for unsteady flow and temperature
simulations in co-rotating twin-screw extruders. Spline-based descriptions of
arbitrary screw geometries are generated using Elliptic Grid Generation. They
are evaluated in a number of discrete points to yield a coarse classical mesh.
The use of a special control mapping allows to fine-tune properties of the
coarse mesh like orthogonality at the boundaries. The coarse mesh is used as a
'scaffolding' to generate a boundary-conforming mesh out of a fine background
mesh at run-time. Storing only a coarse mesh makes the method cheap in terms of
memory storage. Additionally, the adaptation at run-time is extremely cheap
compared to computing the flow solution. Furthermore, this method circumvents
the need for expensive re-meshing and projections of solutions making it
efficient and accurate. It is incorporated into a space-time finite element
framework. We present time-dependent test cases of non-Newtonian fluids in 2D
and 3D for complex screw designs. They demonstrate the potential of the method
also for arbitrarily complex industrial applications
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