Adaptive remeshing for compressible flow computations
Journal of Computational Physics
Optimal triangular mesh generation by coordinate transformation
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific and Statistical Computing
Variants of BICGSTAB for matrices with complex spectrum
SIAM Journal on Scientific Computing
On the shape of tetrahedra from bisection
Mathematics of Computation
Grid adaption based on modified anisotropic diffusion equations formulated in the parametric domain
Journal of Computational Physics
Delaunay mesh generation governed by metric specifications. Part I algorithms
Finite Elements in Analysis and Design
Delaunay mesh generation governed by metric specifications. Part II. applications
Finite Elements in Analysis and Design
A Local Problem Error Estimator for Anisotropic Tetrahedral Finite Element Meshes
SIAM Journal on Numerical Analysis
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A New Finite Element Gradient Recovery Method: Superconvergence Property
SIAM Journal on Scientific Computing
Measuring Mesh Qualities and Application to Variational Mesh Adaptation
SIAM Journal on Scientific Computing
Applied Numerical Mathematics
An anisotropic mesh adaptation method for the finite element solution of variational problems
Finite Elements in Analysis and Design
High-order sonic boom modeling based on adaptive methods
Journal of Computational Physics
Error estimation and anisotropic mesh refinement for 3d laminar aerodynamic flow simulations
Journal of Computational Physics
Journal of Computational Physics
Mathematics and Computers in Simulation
Original Articles: 3D Metric-based anisotropic mesh adaptation for vortex capture
Mathematics and Computers in Simulation
Continuous Mesh Framework Part I: Well-Posed Continuous Interpolation Error
SIAM Journal on Numerical Analysis
Continuous Mesh Framework Part II: Validations and Applications
SIAM Journal on Numerical Analysis
Monotonic solution of heterogeneous anisotropic diffusion problems
Journal of Computational Physics
Metric tensors for the interpolation error and its gradient in Lp norm
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.48 |
It has been amply demonstrated that significant improvements in accuracy and efficiency can be gained when a properly chosen anisotropic mesh is used in the numerical solution for a large class of problems which exhibit anisotropic solution features. In practice, an anisotropic mesh is commonly generated as a quasi-uniform mesh in the metric determined by a tensor specifying the shape, size, orientation of elements. Thus, it is crucial to choose an appropriate metric tensor for anisotropic mesh generation and adaptation. In this paper, we develop a general formula for the metric tensor for use in any spatial dimension. The formulation is based on error estimates for polynomial preserving interpolation on simiplicial elements. Numerical results in two-dimensions are presented to demonstrate the ability of the metric tensor to produce anisotropic meshes with correct mesh concentration and good overall quality. The procedure developed in this paper for defining the metric tensor can also be applied to other types of error estimates.