Numerical solutions obtained by the Meshless Local Petrov-Galerkin (MLPG) method are presented for two dimensional steady-state heat conduction problems. The MLPG method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. The penalty method is adopted to efficiently enforce the essential boundary co...

We present a new definition of an implicit surface over a noisy point cloud, based on the weighted least squares approach. It can be evaluated very fast, but artifacts are significantly reduced. We propose to use a different kernel function that approximates geodesic distances on the surface by utilizing a geometric proximity graph. From a variety of possibilities, we have examined the Delaunay...

This paper addresses the problem of removing the noise from noisy points clouds in the context of surface reconstruction. We introduce a new smoothing operator Q inspired by the moving least-squares method and robust statistics theory. Our method can be seen as an improvement of the moving least-squares method to preserve sharp features. We also present effective numerical optimization algorith...

In vector field analysis, saddle points have two different types of invariant manifolds, namely stable ones and unstable ones. The invariant manifolds represent separatrices that partition the domain of trajectories into invariant regions of different dynamics. In this work, we analyze the basins of attraction of two different stable nodes by reconstructing the separatrices of a saddle point. T...

In this study, we propose to approximate the a− n relation as well as the da/dn−∆K relation, in fatigue crack propagation, by using the Moving Least Squares (MLS) method. This simple approach can avoid the internal inconsistencies caused by the celebrated Paris’ power law approximation of the da/dn−∆K relation, as well as the error caused by a simple numerical differentiation of the noisy data ...

We study the performance of various agent strategies in an artificial investment scenario. Agents are equipped with a budget, $x(t)$, and at each time step invest a particular fraction, $q(t)$, of their budget. The return on investment (RoI), $r(t)$, is characterized by a periodic function with different types and levels of noise. Risk-avoiding agents choose their fraction $q(t)$ proportional t...

Creating models of real scenes is a complex task for which the use of traditional modelling techniques is inappropriate. For this task, laser rangefinders are frequently used to sample the scene from several viewpoints, with the resulting range images integrated into a final model. In practice, due to surface reflectance properties, occlusions and accessibility limitations, certain areas of the...

In current study, The Mesh-free method based on weak-form formulation coupled with the ultrasound imaging technique is developed. This problem consists in computing the deformation of an elastic non-homogenous phantom by numerical methods (both Mesh-free and Finite Element) and converge their results to the measured deformation by the ultrasound. The shape functions of Mesh-free are approximate...

Rapid advancement of 3D sensing techniques has led to dense and accurate point cloud of an object to be readily available. The growing use of such scanned point sets in product design, analysis, and manufacturing necessitates research on direct processing of point set surfaces. In this paper, we present an approach that enables the direct layered manufacturing of point set surfaces. This new ap...

We develop and analyze a least squares procedure for approximating the homogeneous Dirichlet problem for the wave equation in a bounded domain SI in R . This procedure is based on the pure implicit scheme for time differencing. Surprisingly, it is the normal derivative of u rather than u itself which must be included in the boundary functional. This normal derivative is an unknown quantity. We ...