This paper presents a new method for surface mesh simplification. Given an initial surface mesh (denoted as reference mesh), the goal is to reduce the number of mesh elements while preserving the geometric approximation as well as the shape quality of the resulting mesh. Two tolerance areas with respect to the reference mesh have been introduced to preserve the geometry of the surface. The refe...

A finite element method for elasticity systems with discontinuities in the coefficients and the flux across an arbitrary interface is proposed in this paper. The method is based on a Cartesian mesh with local modifications to the mesh. The total degrees of the freedom of the finite element method remains the same as that of the Cartesian mesh. The local modifications lead to a quasi-uniform bod...

This paper presents a fracture mapping (FM) approach combined with the extended finite element method (XFEM) to simulate coupled deformation and fluid flow in fractured porous media. Specifically, the method accurately represents the impact of discrete fractures on flow and deformation, although the individual fractures are not part of the finite element mesh. A key feature of FM-XFEM is its ab...

Catmull-Clark subdivision scheme provides a powerful method for building smooth and complex surfaces. But the number of faces in the uniformly refined meshes increases sharply with respect to subdivision depth. This paper presents an adaptive subdivision technique as a solution to this problem. Instead of subdivision depths of mesh faces, the adaptive subdivision process is driven by labels of ...

We present a theoretical framework for developing parallel guaranteed quality Delaunay mesh generation software, that allows us to use commercial off-the-shelf sequential Delaunay meshers for two-dimensional geometries. In this paper, we describe our approach for constructing uniform meshes, in other words, the meshes in which all elements have approximately the same size. Our uniform distribut...

We present a new fast method for 3D facial expression tracking based on piecewise non-rigid deformations. Our method takes as input a video-rate sequence of face meshes that record the shape and timevarying expressions of a human face, and deforms a source mesh to match each input mesh to output a new mesh sequence with the same connectivity that reflects the facial shape and expressional varia...

Wireless mesh networks (WMNs) consist of mesh routers and mesh clients where fixed mesh routers form the multi-hop backbone of the network. It is often assumed that each individual mesh client will faithfully follow the prescribed protocols. However, these mobile devices, owned by individual users, will likely do what is the most beneficial to their owners, i.e. act ‘selfishly’. In this article...

Since the finite element approximations of microstructures are strongly mesh dependent, the use of the mesh transformation method based on the energy minimizing principle is considered a natural approach in the finite element computation of microstructures. However, without a control on the mesh quality, the mesh can become increasingly irregular in the process of energy minimization and thus j...

A method for generating geometric surface meshes from a discrete surface, called a reference mesh, is presented. First, the geometrical singularities are extracted from the reference mesh. Then, an almost smooth surface interpolating the reference mesh vertices is associated to the reference mesh. Finally, the reference mesh is adaptively refined via the smooth geometry in order to obtain an ad...