Numerical grid generation: foundations and applications
Numerical grid generation: foundations and applications
Application of Bubnov-Galerkin formulation to orthogonal grid generation
Journal of Computational Physics
Parallel Newton--Krylov--Schwarz Algorithms for the Transonic Full Potential Equation
SIAM Journal on Scientific Computing
An object-oriented framework for block preconditioning
ACM Transactions on Mathematical Software (TOMS)
Automatic Mesh Generation: Applications to Finite Element Methods
Automatic Mesh Generation: Applications to Finite Element Methods
Reference Jacobian optimization-based rezone strategies for arbitrary Lagrangian Eulerian methods
Journal of Computational Physics
Delaunay refinement algorithms for triangular mesh generation
Computational Geometry: Theory and Applications
Unstructured surface mesh adaptation using the Laplace-Beltrami target metric approach
Journal of Computational Physics
Efficient nonlinear solvers for Laplace-Beltrami smoothing of three-dimensional unstructured grids
Computers & Mathematics with Applications
Hi-index | 31.45 |
The finite element method is applied to grid smoothing for two-dimensional planar geometry. The coordinates of the grid nodes satisfy two quasi-linear elliptic equations in the form of Laplace equations in a Riemann space. By forming a Dirichlet boundary value problem, the proposed method is applicable to both structured and unstructured grids. The Riemannian metric, acting as a driving force in the grid smoothing, is computed iteratively beginning with the metric of the unsmoothed grid. Smoothing is achieved by computing the metric tensor on the dual mesh elements, which incorporates the influence of neighbor elements. Numerical examples of this smoothing methodology, demonstrating the efficiency of the proposed approach, are presented.