The meshless method plays an important role in solving problems in computational mechanics where conventional computational methods are not well suited. In this paper, we examine the property of the kernel matrix and investigate the convergence and timing performance of some well-known Krylov subspace methods on solving linear systems from meshless discretizations.

Over the past two decades meshless methods have attracted much attention owing to their advantages in adaptivity, higher degree of solution field continuity, and capability to handle moving boundary and changing geometry. In this work, a meshless integral method based on the regularized boundary integral equation has been developed and applied to two-dimensional linear elasticity and elastoplas...

─ Although many numerical methods have been developed to calculate photonic bandgap structure properties, but always improvement in numerical methods is necessary to have more efficient, accurate and flexible techniques. In the present work, novel periodic meshless shape functions including so-called direct and radial shape functions are presented. The meshless approaches, based on these period...

Keywords: Meshless method Coupled radiative–conductive transfer Discrete ordinates Even parity Complex geometries a b s t r a c t A meshless method DAM is employed to solve the coupled radiative and conductive heat transfer problem in a semi-transparent medium enclosed in complex 2D and 3D geome-tries. The meshless method for radiative transfer is based on the even parity formulation of the dis...

Since meshless methods have been introduced to alleviate the difficulties arising in conventional finite element method, many papers on applications of meshless methods to boundary element method have been published. However, most of these papers use moving least squares approximation functions that have difficulties in prescribing essential boundary conditions. Recently, in order to strengthen...

Purpose – In this paper, a modified meshless method, as one of the numerical techniques that has recently emerged in the area of computational electromagnetics, is extended to solving time-domain wave equation. The paper aims to discuss these issues. Design/methodology/approach – In space domain, the fields at the collocation points are expanded into a series of new Shepard’s functions which ha...

Abstract: A meshless method based on radial point interpolation was recently developed as an effective tool for solving partial differential equations, and has been widely applied to a number of different problems. In addition to the primary advantage of the meshless methods that the computation is performed without any connectivity information between field nodes, the radial point interpolatio...