Surfaces generated by moving least squares methods
Peter Lancaster,K. Salkauskas +1 more
TLDR
In this article, an analysis of moving least squares (m.l.s.) methods for smoothing and interpolating scattered data is presented, in particular theorems concerning the smoothness of interpolants and the description of m. l.s. processes as projection methods.Abstract:
An analysis of moving least squares (m.l.s.) methods for smoothing and interpolating scattered data is presented. In particular, theorems are proved concerning the smoothness of interpolants and the description of m.l.s. processes as projection methods. Some properties of compositions of the m.l.s. projector, with projectors associated with finiteelement schemes, are also considered. The analysis is accompanied by examples of univariate and bivariate problems.read more
Citations
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Journal ArticleDOI
The design and analysis of computer experiments
TL;DR: This paper presents a meta-modelling framework for estimating Output from Computer Experiments-Predicting Output from Training Data and Criteria Based Designs for computer Experiments.
Journal ArticleDOI
Element‐free Galerkin methods
Ted Belytschko,Y. Y. Lu,L. Gu +2 more
TL;DR: In this article, an element-free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems, where moving least-squares interpolants are used to construct the trial and test functions for the variational principle.
Journal ArticleDOI
Meshless methods: An overview and recent developments
TL;DR: Meshless approximations based on moving least-squares, kernels, and partitions of unity are examined and it is shown that the three methods are in most cases identical except for the important fact that partitions ofunity enable p-adaptivity to be achieved.
Journal ArticleDOI
Reproducing kernel particle methods
TL;DR: A new continuous reproducing kernel interpolation function which explores the attractive features of the flexible time-frequency and space-wave number localization of a window function is developed and is called the reproducingkernel particle method (RKPM).
Journal ArticleDOI
Design and analysis of computer experiments
Sonja Kuhnt,David M. Steinberg +1 more
TL;DR: The included papers present an interesting mixture of recent developments in the field as they cover fundamental research on the design of experiments, models and analysis methods as well as more applied research connected to real-life applications.
References
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Proceedings ArticleDOI
A two-dimensional interpolation function for irregularly-spaced data
TL;DR: In many fields using empirical areal data there arises a need for interpolating from irregularly-spaced data to produce a continuous surface as discussed by the authors, and it is assumed that a unique number (such as rainfall in meteorology, or altitude in geography) is associated with each data point.
Journal ArticleDOI
Smooth interpolation of large sets of scattered data
Richard Franke,Greg Nielson +1 more
TL;DR: Methods for solving the following data fitting problems are discussed: Given the data (xi,yi,fi), i = 1,...,N construct a smooth bivariate function S with the property that S(xi, Yi) = fi, i = 2, N.
Journal ArticleDOI
Drawing Contours from Arbitrary Data Points
TL;DR: This paper describes a computer method for drawing, on an incremental plotter, a set of contours when the height is available only for some arbitrary collection of points, based on a distance-weighted, least-squares approximation technique, suitable not only for mathematically derived data, but also for data of geographical and other non-mathematical origins.
Journal ArticleDOI
Piecewise Quadratic Approximations on Triangles
M. J. D. Powell,M. A. Sabin +1 more
TL;DR: Two methods of constructing piecewise quadratic approximations are described which have the property that, if they are applied on each triangle of a triangulation, then ~(x, y) and its first derivatives are continuous everywhere.
Book ChapterDOI
Representation and Approximation of Surfaces
TL;DR: This paper discusses “Coons patches”, defined over squares and triangles, as well as generalizations of these methods, and considers interpolation to arbitrarily spaced data and shows how to combine these methods with the patch methods, in order to achieve more smoothness and fairer shapes.