1. Briefly summarize the paper’s contributions. Does it address a new problem? Does it present a new approach? Does it show new types of results?  [AS] This paper presents a new robust moving least squares (MLS) approach to define a surface from a potentially noisy point set. Using techniques from robust statistics to determine neighborhoods used by MLS, this approach produces a piecewise smoo...

The Meshless Finite Volume Method (MFVM) is developed for solving elasto-static problems, through a new Meshless Local Petrov-Galerkin (MLPG) “Mixed” approach. In this MLPG mixed approach, both the strains as well as displacements are interpolated, at randomly distributed points in the domain, through local meshless interpolation schemes such as the moving least squares(MLS) or radial basis fun...

One common problem encountered in many fields is the generation of surfaces based on values at irregularly distributed nodes. To tackle such problems, we present a modified, robust moving least squares (MLS) method for scattered data smoothing and approximation. The error functional used in the derivation of the classical MLS approximation is augmented with additional terms based on the coeffic...

Abstract In this paper, a Moving-Least-Squares (MLS)-based immersed boundary method (IBM) for simulating viscous compressible flows is proposed. For method, the lattice Boltzmann flux solver (LBFS) used to solve flow field on Eulerian mesh and MLS-based IBM introduced in present paper implement condition. The discrete Lagrangian points are represent Solid boundaries. A second-order MLS interpol...

Three different truly Meshless Local Petrov-Galerkin (MLPG) methods are developed for solving 3D elasto-static problems. Using the general MLPG concept, these methods are derived through the local weak forms of the equilibrium equations, by using different test functions, namely, the Heaviside function, the Dirac delta function, and the fundamental solutions. The one with the use of the fundame...

A meshless method based on the local Petrov-Galerkin approach is proposed, to solve boundary and initial value problems of piezoelectric and magnetoelectric-elastic solids with continuously varying material properties. Stationary and transient dynamic 2-D problems are considered in this paper. The mechanical fields are described by the equations of motion with an inertial term. To eliminate the...