Search

A granular structure can be modeled by a parallelepiped containing spherical balls in three dimensions or by a rectangle filled with disks in two dimensions. These grains (spherical balls or disks) are separated by interfaces called grain boundaries and their size correspond to a size distribution, which is obtained experimentally. The geometrical modeling of such a structure consists in determining the repartition of the set of disjoint grains according to these specifications. In this paper, a new constructive algorithm based on an advancing-front approach, usually used in the context of mesh generation, is proposed. This algorithm is nearly linear in complexity, robust and fast in both two and three dimensions. Enhancements in computing time and density are observed and reported via comparisons with existing methods. Moreover, we propose a method to transform spherical balls (disks) into polyhedral (polygonal) cells similar to the real grain shapes. Examples of nanostructure modeling in two and three dimensions are presented. Copyright © 2009 John Wiley & Sons, Ltd.

In the context of composite parametric surface meshing using a direct or an indirect (via the meshing of parametric domains) method, the discretization of interface curves joining patches plays a central part. In the case of an indirect method, the discretization of interface curves must be taken back to parametric spaces. This is usually done using root finding techniques for generally non-linear parametric functions. This paper presents a new linearization technique to determine the above correspondence. In addition, this linearization of interface curves makes it possible to obtain their discretization without explicitly computing the arc length. This method has been implemented in a surface mesh generator and an example from Fluid Mechanics is given to illustrate the pertinence of the proposed approach. Copyright © 2004 John Wiley & Sons, Ltd.

In this paper we discuss an a posteriori interpolation error estimate based on the Hessian of the surface and we propose a new geometric error estimate related to the local deformation of the surface. The new approach makes possible the construction of adapted geometric meshes for surfaces by specifying the element sizes (and directions) so as to bound the error below a user-given threshold value. The surfaces considered here are Cartesian surfaces. An analytical example is provided so as to emphasize the potential of the approach. Copyright © 2003 John Wiley & Sons, Ltd.

An increasingly important part of quantum chemistry involves molecular surfaces. To model such a surface, the basic idea is to assimilate each constituting atom with a simple sphere. Surface mesh generation techniques can then be used for visualization but also for simulation, where mesh quality has a strong influence on solution accuracy. This article presents a new approach to generating quality meshes on arbitrary molecular surfaces (van der Waals, solvent-accessible, or solvent-excluded surfaces). First, a boundary representation (B-rep) of the surface is obtained, i.e., a set of patches and the topological relations between them. Second, an appropriate parameterization is computed for each kind of patch and the user-specified element sizes are converted into an isotropic metric map. Third, meshes of the parametric domains are generated with respect to an induced anisotropic metric map, using a combined advancing-front–generalized Delaunay approach. Finally, these meshes are mapped onto the entire surface. The proposed method has been integrated within the BLMOL mesh generator and application examples are given to illustrate its capabilities. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003

SUMMARY In the boundary representation (B-Rep) model, a three-dimensional (3D) surface is dened by a set of 'simpler surfaces' called 'patches'. Although there are many dierent ways to specify a patch, a common case is that of a 4-sided patch represented by a structured grid of points. For instance, this kind of data can easily be obtained from a CAD system, as it is the mapping of regularly spaced points in a rectangular parametric domain. It can also be obtained from some particular 3D scanning devices. Non-rectangular topologies may also be encountered, for instance the 3-sided patch which can be considered as a degenerate case of the 4-sided patch (one side being of zero length). In this paper, we use the Coons method to build a surface interpolating the vertices of such a grid. The continuity of this parameterization makes it suitable for our indirect approach to surface meshing, which is generally based on the generation of an anisotropic mesh in the parametric space. Moreover, the indirect approach has been extended to the construction of anisotropic geometric surface meshes in 3D space, allowing an accurate geometric representation of the surface with a minimal number of elements. Several examples demonstrate the capabilities of this method. Copyright ? 2003 John Wiley & Sons, Ltd.

Given a boundary surface mesh (a set of triangular facets) of a polyhedron, the problem of deciding whether or not a triangulation exists is reported to be NP-hard. In this paper, an algorithm to triangulate a general polyhedron is presented which makes use of a classical Delaunay triangulation algorithm, a phase for recovering the missing boundary facets by means of facet partitioning, and a final phase that makes it possible to remove the additional points defined in the previous step. Following this phase, the resulting mesh conforms to the given boundary surface mesh. The proposed method results in a discussion of theoretical interest about existence and complexity issues. In practice, however, the method should provide what we call ‘ultimate’ robustness in mesh generation methods. Copyright © 2003 John Wiley & Sons, Ltd.

We deal with adaptive simulation of time-dependent problems. Mesh adaptation for unsteady configurations is especially important as the phenomenon evolves in the whole computational domain and, in order to capture such a phenomenon accurately on adapted meshes, one has to predict the evolution path. Here, we propose a new adaptive algorithm for time-dependent simulation; the idea is to solve a transient fixed problem by introducing a new loop in the adaptation scheme. The metric used for 3D simulations is constructed with an a posteriori error estimate based on a discrete approximation of the Hessian of the solution. For time-dependent simulation, a metric intersection in time is introduced to refine all the areas where the phenomena evolve

An indirect method for meshing parametric surfaces conforming to a user-specifiable size map is presented. First, from this size specification, a Riemannian metric is defined so that the desired mesh is one with unit length edges with respect to the related Riemannian space (the so-called ‘unit mesh’). Then, based on the intrinsic properties of the surface, the Riemannian structure is induced into the parametric space. Finally, a unit mesh is generated completely inside the parametric space such that it conforms to the metric of the induced Riemannian structure. This mesh is constructed using a combined advancing-front—Delaunay approach applied within a Riemannian context. The proposed method can be applied to mesh composite parametric surfaces. Several examples illustrate the efficiency of our approach. Copyright © 2000 John Wiley & Sons, Ltd.

This paper proposes a method to evaluate the size quality as well as the shape quality of constrained surface meshes, the constraint being either a given metric or the geometric metric associated with the surface geometry. In the context of numerical simulations, the metric specifications are those related to the finite element method. The proposed measures allow to validate the surface meshes within a general mesh adaption scheme, the metric map being usually provided via an a posteriori error estimate. Several examples of surface meshes are proposed to illustrate the relevance of the approach. Copyright © 1999 John Wiley & Sons, Ltd.

This paper gives a procedure to control the size variation in a mesh adaption scheme where the size specication (the so-called control space) is used to govern the mesh generation stage. The method consists in replacing the initial control space by a reduced one by means of size or metric. It allows to improve, a priori, the quality of the adapted mesh and to speed up the adaption procedure. Several numerical examples show the eciency of the reduction scheme. ? 1998 John Wiley & Sons, Ltd.

In this paper, we begin by recalling an adaptive mesh generation method governed by isotropic and anisotropic discrete metric maps, by means of the generation of a unit mesh with respect to a Riemannian structure. We propose then an automatic triangular to quadrilateral mesh conversion scheme, which generalizes the standard case to the anisotropic context. In addition, we introduce an optimal vertex smoothing procedure. Application test examples, in particular a CFD test, are given to demonstrate the eciency of the proposed method. ? 1998 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng., 41, 915{934 (1998)

SUMMARY This paper aims to outline the dierent phases necessary to implement a Delaunay-type automatic mesh generator. First, it summarizes this method and then describes a variant which is numerically robust by mentioning at the same time the problems to solve and the dierent solutions possible. The Delaunay insertion process by itself, the boundary integrity problem, the way to create the eld points as well as the optimization procedures are discussed. The two-dimensional situation is described fully and possible extensions to the three-dimensional case are briey indicated. ? 1997 by John Wiley & Sons, Ltd. There exist a large number of papers dealing with 2-D-mesh generation using the Delaunay method (see Reference 1). Nevertheless, we propose a new scheme with ambition to optimize, if possible, the dierent steps used in the practical application of the algorithm. We have tried to develop for each step an optimal solution. The method has been implemented and results show the performance of the algorithm. So we can construct a well-shaped mesh constituted by a million of triangles in a few minutes on a HP 735 workstation. The 2-D case is fully detailed for clarity but most of the results can be extended without diculty in three dimensions. The problem to be solved is to construct a consistent mesh of a domain essentially from its boundary data segments. The resulting mesh will be the support of a nite element computation which can indicate if it is adapted or must be adapted by any method (it is not the goal of this paper). Nevertheless, it is important to begin with a well-shaped mesh knowing that this request can only be based on geometric considerations, since the sole known information is of geometric nature. Thus, the shape and the size of the elements must be consistent with these data.