Results 1  10
of
29
Quality Meshing for Polyhedra with Small Angles
, 2004
"... We present an algorithm to compute a Delaunay mesh conforming to a polyhedron possibly with small input angles. The radiusedge ratio of most output tetrahedra are bounded by a constant, except possibly those that are provably close to small angles. Furthermore, the mesh is not unnecessarily dense i ..."
Abstract

Cited by 32 (8 self)
 Add to MetaCart
(Show Context)
We present an algorithm to compute a Delaunay mesh conforming to a polyhedron possibly with small input angles. The radiusedge ratio of most output tetrahedra are bounded by a constant, except possibly those that are provably close to small angles. Furthermore, the mesh is not unnecessarily dense in the sense that the edge lengths are at least a constant fraction of the local feature sizes at the edge endpoints. This algorithm is simple to implement as it eliminates most of the computation of local feature sizes and explicit protective zones. Our experimental results validate that few skinny tetrahedra remain and they lie close to small acute input angles. 1
A practical Delaunay meshing algorithm for a large class of domains
 Proceedings of the 16th International Meshing Roundtable
, 2007
"... Summary. Recently a Delaunay refinement algorithm has been proposed that can mesh domains as general as piecewise smooth complexes [7]. This class includes polyhedra, smooth and piecewise smooth surfaces, volumes enclosed by them, and above all nonmanifolds. In contrast to previous approaches, the ..."
Abstract

Cited by 31 (7 self)
 Add to MetaCart
(Show Context)
Summary. Recently a Delaunay refinement algorithm has been proposed that can mesh domains as general as piecewise smooth complexes [7]. This class includes polyhedra, smooth and piecewise smooth surfaces, volumes enclosed by them, and above all nonmanifolds. In contrast to previous approaches, the algorithm does not impose any restriction on the input angles. Although this algorithm has a provable guarantee about topology, certain steps are too expensive to make it practical. In this paper we introduce a novel modification of the algorithm to make it implementable in practice. In particular, we replace four tests of the original algorithm with only a single test that is easy to implement. The algorithm has the following guarantees. The output mesh restricted to each manifold element in the complex is a manifold with proper incidence relations. More importantly, with increasing level of refinement which can be controlled by an input parameter, the output mesh becomes homeomorphic to the input while preserving all input features. Implementation results on a disparate array of input domains are presented to corroborate our claims. 1
Lecture Notes on Delaunay Mesh Generation
, 1999
"... purposes notwithstanding any copyright annotation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the ..."
Abstract

Cited by 23 (0 self)
 Add to MetaCart
(Show Context)
purposes notwithstanding any copyright annotation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the
Meshing volumes bounded by smooth surfaces
 Proc. 14th Internat. Meshing Roundtable
, 2005
"... This paper introduces a threedimensional mesh generation algorithm for domains bounded by smooth surfaces. The algorithm combines a Delaunaybased surface mesher with a Ruppertlike volume mesher, to get a greedy algorithm that samples the interior and the boundary of the domain at once. The algori ..."
Abstract

Cited by 23 (2 self)
 Add to MetaCart
This paper introduces a threedimensional mesh generation algorithm for domains bounded by smooth surfaces. The algorithm combines a Delaunaybased surface mesher with a Ruppertlike volume mesher, to get a greedy algorithm that samples the interior and the boundary of the domain at once. The algorithm constructs provablygood meshes, it gives control on the size of the mesh elements through a userde ned sizing eld, and it guarantees the accuracy of the approximation of the domain boundary. A noticeable feature is that the domain boundary has to be known only through an oracle that can tell whether a given point lies inside the object and whether a given line segment intersects the boundary. This makes the algorithm generic enough to be applied to a wide variety of objects, ranging from domains de ned by implicit surfaces to domains de ned by levelsets in 3D greyscaled images or by pointset surfaces. 1
Meshing 3D domains bounded by piecewise smooth surfaces
"... This report provides an algorithm to mesh 3D domains bounded by piecewise smooth surfaces. The algorithm may handle as well subdivisions of the domain forming non manifold surfaces. The boundaries and constraints are assumed to be described as a complex formed by a set of vertices, a set of curved ..."
Abstract

Cited by 20 (2 self)
 Add to MetaCart
This report provides an algorithm to mesh 3D domains bounded by piecewise smooth surfaces. The algorithm may handle as well subdivisions of the domain forming non manifold surfaces. The boundaries and constraints are assumed to be described as a complex formed by a set of vertices, a set of curved segments and a set of surface patches. Each curve segment is assumed to be a piece of a closed smooth curves and each surface patch is assumed to be included in a smooth surface without boundary. The meshing algorithm is a Delaunay refinement and it uses the notion of restricted Delaunay triangulation to approximate the input curved segments and surfaces patches. The algorithm is shown to end up with a set of vertices whose restricted Delaunay triangulation to any input feature forms an homeomorphic and accurate approximation of this feature. The algorithm also provides guarantees on the size and shape of facets approximating the input surface patches and on the size and shape of the tetrahedra in the domain. In its actual state the algorithm suffers from a severe angular restriction on input constraints. It basically assumes that linear subspaces which are tangent to distinct input features on a common point form angles measuring at least 90 degrees.
Weighted Delaunay Refinement for Polyhedra with Small Angles
 the Proceeding of the Fourth International Meshing Roundtable
, 2005
"... Abstract Recently, a provable Delaunay meshing algorithm called QMesh has been proposed forpolyhedra that may have acute input angles. The algorithm guarantees bounded circumradius to shortest edge length ratio for all tetrahedra except the ones near small input angles. Thisguarantee eliminates or l ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
(Show Context)
Abstract Recently, a provable Delaunay meshing algorithm called QMesh has been proposed forpolyhedra that may have acute input angles. The algorithm guarantees bounded circumradius to shortest edge length ratio for all tetrahedra except the ones near small input angles. Thisguarantee eliminates or limits the occurrences of all types of poorly shaped tetrahedra except slivers. A separate technique called weight pumping is known for sliver elimination. But,allowable input for the technique so far have been periodic point sets and piecewise linear complex with nonacute input angles. In this paper, we incorporate the weight pumping methodinto QMesh thereby ensuring that all tetrahedra except the ones near small input angles havebounded aspect ratio. Theoretically, the algorithm has an abysmally small angle guarantee
Delaunay mesh generation of three dimensional domains
, 2007
"... Delaunay meshes are used in various applications such as finite element analysis, computer graphics rendering, geometric modeling, and shape analysis. As the applications vary, so do the domains to be meshed. Although meshing of geometric domains with Delaunay simplices have been around for a while, ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
Delaunay meshes are used in various applications such as finite element analysis, computer graphics rendering, geometric modeling, and shape analysis. As the applications vary, so do the domains to be meshed. Although meshing of geometric domains with Delaunay simplices have been around for a while, provable techniques to mesh various types of three dimensional domains have been developed only recently. We devote this article to presenting these techniques. We survey various related results and detail a few core algorithms that have provable guarantees and are amenable to practical implementation. Delaunay refinement, a paradigm originally developed for guaranteeing shape quality of mesh elements, is a common thread in these algorithms. We finish the article by listing a set of open questions.
3D phasefield simulations of interfacial dynamics in Newtonian and viscoelastic fluids
 J. Comput. Phys
, 2010
"... Abstract This work presents a threedimensional finiteelement algorithm, based on the phasefield model, for computing interfacial flows of Newtonian and complex fluids. A 3D adaptive meshing scheme produces fine grid covering the interface and coarse mesh in the bulk. It is key to accurate resolu ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
Abstract This work presents a threedimensional finiteelement algorithm, based on the phasefield model, for computing interfacial flows of Newtonian and complex fluids. A 3D adaptive meshing scheme produces fine grid covering the interface and coarse mesh in the bulk. It is key to accurate resolution of the interface at manageable computational costs. The coupled NavierStokes and CahnHilliard equations, plus the constitutive equation for nonNewtonian fluids, are solved using secondorder implicit time stepping. Within each time step, Newton iteration is used to handle the nonlinearity, and the linear algebraic system is solved by preconditioned Krylov methods. The phasefield model, with a physically diffuse interface, affords the method several advantages in computing interfacial dynamics. One is the ease in simulating topological changes such as interfacial rupture and coalescence. Another is the capability of computing contact line motion without invoking ad hoc slip conditions. As validation of the 3D numerical scheme, we have computed drop deformation in an elongational flow, relaxation of a deformed drop to the spherical shape, and drop spreading on a partially wetting substrate. The results are compared with numerical and experimental results in the literature as well as our own axisymmetric computations where