High-order spline interpolations in the particle simulation
Journal of Computational Physics
Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Computer simulation using particles
Computer simulation using particles
FLIP MHD: a particle-cell method for magnetohydrodynamics
Journal of Computational Physics
On particle-grid interpolation and calculating chemistry in particle-in-cell methods
Journal of Computational Physics
An analysis of 1-D smoothed particle hydrodynamics kernels
Journal of Computational Physics
Inviscid axisymmetrization of an elliptical vortex
Journal of Computational Physics
Evaluation and Design of Filters Using a Taylor Series Expansion
IEEE Transactions on Visualization and Computer Graphics
Remeshed smoothed particle hydrodynamics for the simulation of viscous and heat conducting flows
Journal of Computational Physics
Remeshed smoothed particle hydrodynamics for the simulation of laminar chemically reactive flows
Journal of Computational Physics
Advances in direct numerical simulations of 3D wall-bounded flows by Vortex-in-Cell methods
Journal of Computational Physics
MOMS: maximal-order interpolation of minimal support
IEEE Transactions on Image Processing
Hi-index | 31.45 |
We present a methodology of high order accuracy that constructs in a systematic way functions which can be used for the accurate interpolation and differentiation of scattered data. The functions are based on linear combination of polynomials (herein B-splines are used). The technique is applied to one-dimensional datasets but can be extended as needed for multidimensional interpolation and differentiation. The methodology can also construct one-sided functions for high-order interpolation and differentiation. The constructed functions possess compact support. The penalty for the high order of accuracy is the need to solve a system of L × L equations where L is the order of the approximation. In order to have a robust solution of the L × L system the singular value decomposition technique was adopted. The proposed technique can also be applied in the context of other methods, in order to increase their accuracy. The main novel features of the technique are that no grid-based information (connectivity) is necessary and a minimum number of samples are required to achieve the desired order of approximation. The order of the approximation is not affected when more samples than the minimum necessary are added in the domain of influence.