Error estimates for interpolation by compactly supported radial basis functions of minimal degree
Journal of Approximation Theory
On the smoothness of positive definite and radial functions
Journal of Computational and Applied Mathematics
Smooth surface reconstruction from noisy range data
Proceedings of the 1st international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Algebraic mesh quality metrics for unstructured initial meshes
Finite Elements in Analysis and Design
A semi-torsional spring analogy model for updating unstructured meshes in 3D moving domains
Finite Elements in Analysis and Design
Journal of Computational Physics
Benchmark problems for incompressible fluid flows with structural interactions
Computers and Structures
Multicloud: Multigrid convergence with a meshless operator
Journal of Computational Physics
Efficient mesh motion using radial basis functions with data reduction algorithms
Journal of Computational Physics
Journal of Computational Physics
Finite Elements in Analysis and Design
Performance of partitioned procedures in fluid-structure interaction
Computers and Structures
A reduced domain strategy for local mesh movement application in unstructured grids
Applied Numerical Mathematics
Proceedings of the 2010 Conference on Grand Challenges in Modeling & Simulation
A fast mesh deformation method using explicit interpolation
Journal of Computational Physics
Presence: Teleoperators and Virtual Environments
A complete framework for 3D mesh morphing
Proceedings of the 11th ACM SIGGRAPH International Conference on Virtual-Reality Continuum and its Applications in Industry
Journal of Computational Physics
Fast dimensional inspection of deformable parts from partial views
Computers in Industry
Journal of Scientific Computing
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A new mesh movement algorithm for unstructured grids is developed which is based on interpolating displacements of the boundary nodes to the whole mesh with radial basis functions (RBF's). A small system of equations, only involving the boundary nodes, has to be solved and no grid-connectivity information is needed. The method can handle large mesh deformations caused by translations, rotations and deformations, both for 2D and 3D meshes. However, the performance depends on the used RBF. The best accuracy and robustness with the highest efficiency are obtained with a C^2 continuous RBF with compact support, closely followed by the thin plate spline. The deformed meshes are suitable for flow computations as is shown by performing calculations around a NACA-0012 airfoil.