In this paper we analyze a parallel version of a multilevel red/green local refinement algorithm for tetrahedral meshes. The refinement method is similar to the approaches used in the UG-package [33] and by Bey [11, 12]. We introduce a new data distribution format that is very suitable for the parallel multilevel refinement algorithm. This format is called an admissible hierarchical decompositi...

The Zienkiewicz—Zhu error estimate is slightly modified for the hierarchical p-refinement, and is then applied to three plane elastostatic problems to demonstrate its effectiveness. In each case, the error decreases rapidly with an increase in the number of degrees of freedom. Thus Zienkiewicz—Zhu’s error estimate can be used in the hp-refinement of finite element meshes. ( 1999 Elsevier Scienc...

The paper proposes goal-oriented error estimation and mesh refinement for optimal control problems with elliptic PDE constraints using the value of the reduced cost functional as quantity of interest. Error representation, hierarchical error estimators, and greedy-style error indicators are derived and compared to their counterparts when using the all-at-once cost functional as quantity of inte...

We develop an a posteriori error estimate of hierarchical type for Dirichlet eigenvalue problems of the form (−∆ + (c/r))ψ = λψ on bounded domains Ω, where r is the distance to the origin, which is assumed to be in Ω. This error estimate is proven to be asymptotically identical to the eigenvalue approximation error on a family of geometrically-graded meshes. Numerical experiments demonstrate th...

We build on state of the art methods for multiresolution embedded coding of images, such as Said and Pearlman’s Set Partitioning In Hierarchical Trees, and combine them with ideas for 3D objects modelling with subdivision surfaces, to obtain a new technique for hierarchical 3D model coding. The compression ratios we obtain are better than or similar to previously reported ones but, perhaps more...

We describe a pointerless representation of hierarchical regular simplicial meshes, based on a bisection approach proposed by Maubach. We introduce a new labeling scheme, called an LPT code, which uniquely encodes the geometry of each simplex of the hierarchy, and we present rules to compute the neighbors of a given simplex efficiently through the use of these codes. In addition, we show how to...

This paper presents a voxel-based biomechanical model for muscle deformation using finite element method (FEM) and volume graphics. Hierarchical voxel meshes are reconstructed from filtered segmented muscle images followed by FEM simulation and volume rendering. Physiological muscle force is considered and linear elastic muscle models for both static and dynamic cases are simulated by FEM. Voxe...

We present in this paper a new approach to detect and precisely report the collisions and contacts between deformable moving bodies and their environment. The moving bodies are sampled as meshes whose vertices are followed up in a convex subdivision of the surrounding space. Particles are continuously spanned along the edges to detect collisions with cells of this subdivision. We report experim...

This paper introduces an optimal hierarchical adaptive mesh construction algorithm using the Face-Centered Orthorhombic lattice (FCO) sampling which is a natural extension of the quincunx lattice to the 3-dimensional case. A scheme for construction of adaptive meshes is presented. Initially, a highly detailed and densely sampled regular mesh is obtained from geometry scanning or from a non opti...

In this paper, we present a method for deformable object tracking that exploits the entire image information using the optical flow equation instead of working with discrete feature points. Our method starts from the optical flow constraint and first estimates global transformations in a hierarchical framework. Elastic deformations are then estimated separately using deformable meshes and spati...