Curvilinear mesh adaptation using radial basis function interpolation and smoothing

DOI10.1007/s10915-018-0711-0OpenAlexW2963838206WikidataQ129977664 ScholiaQ129977664MaRDI QIDQ1632267

Robert M. Kirby, Shankar P. Sastry, Vidhi Zala, Varun Shankar

Publication date: 13 December 2018

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.03358

zbMATH Keywords

conformal mappingradial basis functionsmesh adaptationmesh qualitymesh deformationcurvilinear mesh generation

Mathematics Subject Classification ID

Interpolation in approximation theory (41A05) Moment problems and interpolation problems in the complex plane (30E05) Numerical analysis (65-XX)

Uses Software

• Matlab
• DistMesh
• rbf_qr

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Robust untangling of curvilinear meshes
• A high-order kernel method for diffusion and reaction-diffusion equations on surfaces
• CAD and mesh repair with radial basis functions
• Stable calculation of Gaussian-based RBF-FD stencils
• A numerical study of some radial basis function based solution methods for elliptic PDEs
• On the role of polynomials in RBF-FD approximations. I: Interpolation and accuracy
• A constrained optimization approach to finite element mesh smoothing
• Interpolation in the limit of increasingly flat radial basis functions
• An isoparametric approach to high-order curvilinear boundary-layer meshing
• Stable computation of multiquadric interpolants for all values of the shape parameter
• An algorithm for coarsening unstructured meshes
• A radial basis function (RBF)-finite difference (FD) method for diffusion and reaction-diffusion equations on surfaces
• Multivariate interpolation by polynomials and radial basis functions
• The Runge phenomenon and spatially variable shape parameters in RBF interpolation
• Theoretical and computational aspects of multivariate interpolation with increasingly flat radial basis functions
• Algebraic Mesh Quality Metrics
• Scattered Data Interpolation on Embedded Submanifolds with Restricted Positive Definite Kernels: Sobolev Error Estimates
• Stable Evaluation of Gaussian Radial Basis Function Interpolants
• Green’s Functions: Taking Another Look at Kernel Approximation, Radial Basis Functions, and Splines
• Stable Computations with Gaussian Radial Basis Functions
• A Stable Algorithm for Flat Radial Basis Functions on a Sphere
• An apporach to automatic three-dimensional finite element mesh generation
• Laplacian smoothing and Delaunay triangulations
• A generic Delaunay triangulation algorithm for finite element meshes
• A Simple Mesh Generator in MATLAB
• On advancing front mesh generation in three dimensions
• A radial basis function (RBF) finite difference method for the simulation of reaction–diffusion equations on stationary platelets within the augmented forcing method
• Three‐dimensional adaptive finite element computations and applications to non‐Newtonian fluids
• Symmetrical Joukowsky airfoils in shear flow