Local modification of meshes for adaptive and/or multigrid finite-element methods
Journal of Computational and Applied Mathematics
Local bisection refinement for N-simplicial grids generated by reflection
SIAM Journal on Scientific Computing
A recursive approach to local mesh refinement in two and three dimensions
Journal of Computational and Applied Mathematics
Parallel Algorithms for Adaptive Mesh Refinement
SIAM Journal on Scientific Computing
Using generic programming for designing a data structure for polyhedral surfaces
Computational Geometry: Theory and Applications - Special issue on applications and challenges
Numerical parameterization of curves and surfaces
Computer Aided Geometric Design
A 3D refinement/derefinement algorithm for solving evolution problems
Applied Numerical Mathematics - Special issue on numerical grid generation-technologies for advanced simulations
Automatic mesh pre-optimization based on the geometric discretization error
Advances in Engineering Software
Locally Adapted Tetrahedral Meshes Using Bisection
SIAM Journal on Scientific Computing
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The purpose of this paper is twofold. First we introduce improved versions of our algorithms for refining and coarsening 2D and 3D nested triangular and tetrahedral grids, and secondly the application of these algorithms in the simulation of 2D and 3D problems, is demonstrated. A key idea of the algorithms is the use of the topological concept of the skeleton of a triangulation in two or three dimensions in order to reduce the dimension of the refinement problem in a natural hierarchic manner.Improved skeleton based refinement (SBR) algorithms and their counterpart, the skeleton based derefinement (SBD) algorithms are described in this study. The algorithms are fully automatic and are applied here to a 2D boundary value problem, a 3D approximation problem with a large gradient, a geometric shape modeling problem and a simulation evolution problem in 3D.