This paper introduces the use of moving least-squares (MLS) approximations for the development of high-order finite volume discretizations on unstructured grids. The field variables and their successive derivatives can be accurately reconstructed using this mesh-free technique in a general nodal arrangement. The methodology proposed is used in the construction of two numerical schemes for the s...

We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). The computation of points on the surface is local, which results in an out-of-core technique that can h...

(2001) A Meshless Local Petrov-Galerkin (MLPG) method for free and forced vibration analyses for solids. Abstract The Meshless Local Petrov-Galerkin (MLPG) method is an effective truly meshless method for solving partial differential equations using Moving Least Squares (MLS) interpolants and local weak forms. In this paper, a MLPG formulation is proposed for free and forced vibration analyses....

In this paper, we target enhanced 3D reconstruction of non-rigidly deforming objects based on a view-independent surface representation with an automated recursive filtering scheme. This work improves upon the KinectDeform algorithm which we recently proposed. KinectDeform uses an implicit viewdependent volumetric truncated signed distance function (TSDF) based surface representation. The view-...

Approximations of non-smooth multivariate functions return low-order approximations in the vicinities of the singularities. Most prior works solve this problem for univariate functions. In this work we introduce a method for approximating non-smooth multivariate functions of the form f = g + r+ where g, r ∈ C(R) and the function r+ is defined by r+(y) = { r(y), r(y) ≥ 0 0, r(y) < 0 , ∀y ∈ R . G...

ACKNOWLEDGEMENTS I would like to thank my advisor Dr. Robert E. Bodenheimer for giving me the opportunity to work with him and also for guiding me through the course of my thesis work. I would also like to thank Dr. Benoit Dawant for helping me shape my work and giving valuable suggestions which helped complete this thesis. Last but not the least, I would like to express my thanks to my family ...

The Element free Galerkin method, which is based on the Moving Least Squares approximation, requires only nodal data and no element connectivity, and therefore is more ̄exible than the conventional ®nite element method. Direct imposition of essential boundary conditions for the element free Galerkin (EFG) method is always dif®cult because the shape functions from the Moving Least Squares approx...

This paper presents an efficient meshless method for analyzing cracked piezoelectric structures subjected to mechanical and electrical loading. In this method, an element free Galerkin (EFG) formulation, an enriched basic function and some special shape functions that contain discontinuous derivatives are employed. Based on the moving least squares (MLS) interpolation approach, the EFG method i...

The standard approaches to solving overdetermined linear systems Ax ≈ b construct minimal corrections to the vector b and/or the matrix A such that the corrected system is compatible. In ordinary least squares (LS) the correction is restricted to b, while in data least squares (DLS) it is restricted to A. In scaled total least squares (Scaled TLS) [15], corrections to both b and A are allowed, ...

Recent development of laser scanning device increased the capability of representing rock outcrop in a very high resolution. Accurate 3D point cloud model with rock joint information can help geologist to estimate stability of rock slope on-site or off-site. An automatic plane extraction method was developed by computing normal directions and grouping them in similar direction. Point normal was...