Catálogo de publicaciones - libros

This paper introduces a three-dimensional mesh generation algorithm for domains bounded by smooth surfaces. The algorithm combines a Delaunaybased surface mesher with a Ruppert-like volume mesher, to get a greedy algorithm that samples the interior and the boundary of the domain at once. The algorithm constructs provably-good meshes, it gives control on the size of the mesh elements through a user-defined sizing field, 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 defined by implicit surfaces to domains defined by level-sets in 3D grey-scaled images or by point-set surfaces.

Problem of tetrahedral meshing of three-dimensional domains whose boundaries are curved surfaces is wide open. Traditional approach consists in an approximation of curved boundaries by piecewise linear boundaries before mesh generation. As the result mesh quality may deteriorate. This paper presents a technique for Delaunay-based tetrahedralization in which a set of constrained facets is formed dynamically during face recovery and mechanisms for mutual retriangulation of the curved faces and the tetrahedralization are suggested. The proposed algorithm is constructed in such a way that a facet that was once added in the set of constrained facets is never split into small triangles. It allows retaining the high quality of surface mesh in the tetrahedralization, because during boundary recovery the surface mesh on the curved faces and the tetrahedralization are refined conjointly.

Consistent and accurate representation of geometry is required by a number of applications such as mesh generation, rapid prototyping, manufacturing, and computer graphics. Unfortunately, faceted Computer Aided Design (CAD) models received by downstream applications have many issues that pose problems for their successful usability. Automatic or semi-automatic tools are needed to process the geometry to make it suitable for these downstream applications. An algorithm is presented to detect commonly found geometrical and topological issues in the faceted geometry and process them with minimum user interaction. The present algorithm is based on the iterative vertex pair contraction and expansion operations called stitching and filling respectively. The combination of generality, accuracy, and efficiency of this algorithm seems to be a significant improvement over existing techniques. Results are presented showing the effectiveness of the algorithm to process two- and three-dimensional configurations.

This paper describes a method for extracting feature edges of a polygonal surface for mesh generation. This method can extract feature edges from a polygonal surface typically created by a CAD facet generator in which typical feature edge extraction methods fail due to severe non-uniformity and anisotropy. The method is based on the technique called “polygon crawling,” which samples a sequence of points on the polygonal surface by moving a point along the polygonal surface. Extracting appropriate feature edges is important for creating a coarse mesh without yielding self-intersections. Extensive tests have been performed with various CAD-generated facet models, and this technique has shown good performance in extracting feature edges.

Having reliable finite element (FE) meshes is one of the basics of reliable FE simulations. As development times i.e. in the car industry are expected to decrease, engineers need to edit and optimise FE meshes without access to the underlying CAD geometry. If meshes are not only locally effected by the editing operation, simple mesh optimisations such as mesh relaxation or local remeshing are not sufficient to make the mesh suitable for numerical simulation again and global remeshing is needed. To avoid the traditionally used time-consuming remeshing strategy, we developed a tool to remesh an FE surface model — taking into account the needs for good FE meshes — via volumes. We first voxelise the surface and then generate a new quad mesh via isosurface extraction and subsequent mesh optimisation. This method provides the opportunity to directly couple editing operations on the volumetrical representation with the remeshing procedure.

This paper deals with structured grid generation using Floater’s parametrization algorithm for surface triangulation. It gives an outline of the algorithm in the context of structured grid generation. Then it explains how the algorithm can be used to generate a structured grid over a singular NURBS surface patch. This is an alternate method to the known carpeting method of reparametrization for structured grid generation over a NURBS surface patch. The paper also explains how to generate a structured grid over a four sided trimmed patch of a facetted surface using the parametrization algorithm. All the procedures are explained using examples.

The first stage in an adaptive finite element scheme (cf. [CAS95, bor1]) consists in creating an initial mesh of a given domain Ω, which is used to perform an initial computation (for example a flow solver). A size specification field is deduced (e.g. at the vicinity of each mesh vertex, the desired mesh size is specified), based on the numerical results. If the mesh does not satisfy the size specification field, then a new constrained mesh, governed by this field, is constructed. The size specification field is usually obtained via an error estimate [FOR, VER96]. Actually, the estimation gives a discrete size specification field. Using an adequate size interpolation over the mesh elements, a continuous field is then obtained. Metrics are commonly used to normalize the mesh size specification to one in any direction (cf. [VAL92]), and are defined as a symmetric positive definite matrix associated to any point of the domain. A classical adaptation loop is: 0 Build a initial mesh $$\mathcal{T}_h^0 $$ 1 loop $$i$$ = 0, ... • Solve your problem on mesh $$\mathcal{T}_h^i $$ • Compute an error indicator , and if the error is small enough then stop. • Compute a metric $$\mathcal{M}^{i + 1} $$ , • Bound, regularize the metric $$\mathcal{M}^{i + 1} $$ , • Compute a new unit mesh $$\mathcal{T}_h^{i + 1} $$ with respect to the new metric. In this kind of algorithm, there are two problematic cases: One) if the minimal mesh size is reached then we generally lose the anisotropy of the mesh in this region. Two) In the adaptation loop, we use a hidden scheme to evaluate the metric, so some-times the mesh size to compute a good approximation of the solution is incompatible with the scheme to get a good approximation of the metric. First, we do the numerical experiment to show this two snags. All the experiments are done with FreeFem++ software , see [freefempp, DAN03]. In this article we present the classical mesh adaptation with metric in section 2. And in section 3 we present the first trouble and some way to solve it. In section 4, a second problem is described and we explain when it occurs.

We have shown that representation of curved surfaces with triangular meshes restricts the use of adaptive methods. For a particular convection-diffusion problem, we have shown numerically that the saturated discretization error is proportional to h ^2 where h is the size of the quasi-uniform mesh approximating the curved surface. We have proposed and analyzed theoretically and numerically a new surface reconstruction technique which improves performance of adaptive methods.

Recently, a provable Delaunay meshing algorithm called QMesh has been proposed for polyhedra 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. This guarantee 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 non-acute input angles. In this paper, we incorporate the weight pumping method into QMesh thereby ensuring that all tetrahedra except the ones near small input angles have bounded aspect ratio. Theoretically, the algorithm has an abysmally small angle guarantee inherited from the weight pumping method. Nevertheless, our experiments show that it produces better angles in practice.