76 research outputs found
Quadrilateral meshes with provable angle bounds
In this paper, we present an algorithm that utilizes a quadtree data structure to construct a quadrilateral mesh for a simple polygonal region in which no newly created angle is smaller than 18.43∘(=arctan(13)) or greater than 171.86∘(=135∘+2arctan(13)). This is the first known result, to the best of our knowledge, on a direct quadrilateral mesh generation algorithm with a provable guarantee on the angles
Quadrilateral meshes with provable angle bounds
In this paper, we present an algorithm that utilizes a quadtree data structure to construct a quadrilateral mesh for a simple polygonal region in which no newly created angle is smaller than 18.43∘(=arctan(13)) or greater than 171.86∘(=135∘+2arctan(13)). This is the first known result, to the best of our knowledge, on a direct quadrilateral mesh generation algorithm with a provable guarantee on the angles
Quadrilateral Meshes with Bounded Minimum Angle
This paper presents an algorithm that utilizes a quadtree to construct a strictly convex quadrilateral mesh for a simple polygonal region in which no newly created angle is smaller than . This is the first known result, to the best of our knowledge, on quadrilateral mesh generation with a provable guarantee on the minimum angle
Quadrilateral Meshes with Bounded Minimum Angle
This paper presents an algorithm that utilizes a quadtree to construct a strictly convex quadrilateral mesh for a simple polygonal region in which no newly created angle is smaller than . This is the first known result, to the best of our knowledge, on quadrilateral mesh generation with a provable guarantee on the minimum angle
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
A geometric mesh smoothing algorithm related to damped oscillations
We introduce a smoothing algorithm for triangle, quadrilateral, tetrahedral
and hexahedral meshes whose centerpiece is a simple geometric triangle
transformation. The first part focuses on the mathematical properties of the
element transformation. In particular, the transformation gives rise directly
to a continuous model given by a system of coupled damped oscillations. Derived
from this physical model, adaptive parameters are introduced and their benefits
presented. The second part discusses the mesh smoothing algorithm based on the
element transformation and its numerical performance on example meshes.Comment: 35 pages, 16 figure
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Choosing corners of rectangles for mapped meshing
Consider mapping a regular i x j quadrilateral mesh of a rectangle onto a surface. The quality of the mapped mesh of the surface depends heavily on which vertices of the surface correspond to corners of the rectangle. The authors problem is, given an n-sided surface, chose as corners four vertices such that the surface resembles a rectangle with corners at those vertices. Note that n could be quite large, and the length and width of the rectangle, i and j, are not prespecified. In general, there is either a goal number or a prescribed number of mesh edges for each bounding curve of the surface. The goals affect the quality of the mesh, and the prescribed edges may make finding a feasible set of corners difficult. The algorithm need only work for surfaces that are roughly rectangular, particular those without large reflex angles, as otherwise an unstructured meshing algorithm is used instead. The authors report on the theory and implementation of algorithms for this problem. They also given an overview of a solution to a related problem called interval assignment: given a complex of surfaces sharing curves, globally assign the number of mesh edges or intervals for each curve such that it is possible to mesh each surface according to its prescribed quadrilateral meshing algorithm, and assigned and user-prescribed boundary mesh edges and corners. They also note a practical, constructive technique that relies on interval assignment that can generate a quadrilateral mesh of a complex of surfaces such that a compatible hexahedral mesh of the enclosed volume exists
Higher-order finite element methods for elliptic problems with interfaces
We present higher-order piecewise continuous finite element methods for
solving a class of interface problems in two dimensions. The method is based on
correction terms added to the right-hand side in the standard variational
formulation of the problem. We prove optimal error estimates of the methods on
general quasi-uniform and shape regular meshes in maximum norms. In addition,
we apply the method to a Stokes interface problem, adding correction terms for
the velocity and the pressure, obtaining optimal convergence results.Comment: 26 pages, 6 figures. An earlier version of this paper appeared on
November 13, 2014 in
http://www.brown.edu/research/projects/scientific-computing/reports/201
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