In 2007, the results from a comparison study of grid based codes and SPH codes on multiphase interactions in compressible fluids were presented [1]. The main conclusion from this study was that whilst the grid codes are able to describe important dynamical instabilities, such as KelvinHelmholtz (KH) and Richtmyer-Meshkov (RM), these processes are poorly described by existing SPH codes. It was l...

In this paper, three dimensional (3D) static and dynamic analysis of thick plates based on the Meshless Local Petrov-Galerkin (MLPG) is presented. Using the kinematics of a three-dimensional continuum, the local weak form of the equilibrium equations is derived. A weak formulation for the set of governing equations is transformed into local integral equations on local sub-domains by using a uni...

Electric potential measurement technique (tomography) was introduced as a nondestructive method to evaluate concrete properties and durability. In this study, numerical meshless method was developed to solve a differential equation which simulates electric potential distribution for concrete with inclusion in two dimensions. Therefore, concrete samples with iron block inclusion in different loc...

In recent years, a variety of meshless methods have been developed to solve partial differential equations in complex domains. Meshless discretize the over scattered points instead grids. Radial basis functions (RBFs) popularly used as high accuracy interpolants function values at locations. this paper, we apply polyharmonic splines (PHS) RBF together with appended polynomial and heat conductio...

In this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. We approximate the exact solution by use of Radial Basis Function(RBF) collocation method. This techniqueplays an important role to reduce a fractional dierential equation to a system of equations. The numerical results demonstrate the accuracy and ability of this me...

By coupling the flexibility of Thin-Plate Splines interpolation with Green’s integral formula, we obtain a meshless cubature method from scattered samples of small/moderate size, on convex as well as nonconvex and even multiply connected polygonal domains. 2000 AMS subject classification: 65D05, 65D32.

This paper proposes a method called meshless parameterization for param eterizing and triangulating single patch unorganized point sets The points are mapped into a planar parameter domain by solving a sparse linear system By making a stan dard triangulation of the parameter points we obtain a corresponding triangulation of the original data set

Title of dissertation: OPTIMAL APPROXIMATION SPACES FOR SOLVING PROBLEMS WITH ROUGH COEFFICIENTS Qiaoluan Li, Doctor of Philosophy, 2009 Dissertation directed by: Professor John E. Osborn Department of Mathematics The finite element method has been widely used to solve partial differential equations by both engineers and mathematicians for the last several decades. This is due to its well-known...

a meshless approach, collocation discrete least square (cdls) method, is extended in this paper, for solvingelasticity problems. in the present cdls method, the problem domain is discretized by distributed field nodes. the fieldnodes are used to construct the trial functions. the moving least-squares interpolant is employed to construct the trialfunctions. some collocation points that are indep...